3 edition of **Cr Submanifolds of Kaehl.& Sasakian Manifolds** found in the catalog.

Cr Submanifolds of Kaehl.& Sasakian Manifolds

Kon/Yano

- 270 Want to read
- 5 Currently reading

Published
**December 1982** by Birkhauser .

Written in English

- General,
- Mathematics

The Physical Object | |
---|---|

Format | Hardcover |

ID Numbers | |

Open Library | OL11388035M |

ISBN 10 | 0817631194 |

ISBN 10 | 9780817631192 |

OCLC/WorldCa | 9066461 |

Submanifolds Vector fields, covector fields, the tensor algebra and tensor fields → In this chapter, we will show what submanifolds are, and how we can obtain, under a condition, a submanifold out of some C n (M) {\displaystyle {\mathcal {C}}^{n}(M)} functions. The geometry of invariant submanifolds M of Sasakian manifolds M is carried out from ’s by M. Kon 1, D. Chinea 2, 3 and B.S. Anitha and C.S. Bagewadi 4. The aurthor 1 has proved that invariant submanifold of Sasakian structure also carries Sasakian structure. In this paper we extend the results to invariant submanifolds. The paper presents some results obtained from the study of anti-invariant submanifolds of trans-Sasakian manifolds. Bibtex entry for this abstract Preferred . In the present paper, we study a new class of submanifolds of a generalized Quasi-Sasakian manifold, called skew semi-invariant submanifold. We obtain integrability conditions of the distributions on a skew semi-invariant submanifold and also find the condition for a skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold to be Cited by: 3.

Abstract. The object of the present paper is to study pseudo-slant submanifolds of trans-Sasakian manifolds. Integrability conditions of the distributions on these submanifolds are worked out. Some interesting results regarding such manifolds have also been deduced. An example of a pseudo-slant submanifold of a trans-Sasakian manifold is given.

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CR Submanifolds of Kaehlerian and Sasakian Manifolds (Progress in Mathematics) Softcover reprint of the original 1st ed. Edition by Kentaro Yano (Author) ISBN ISBN Why is ISBN important. ISBN.

This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Cited by: Let be an almost Hermitian manifold (cf. also Hermitian structure), where is an almost-complex structure on and is a Riemannian metric on satisfying for any vector fields and on.A real submanifold of is said to be a complex (holomorphic) submanifold if the tangent bundle of is invariant under, i.e.

for be the normal bundle is called a totally real (anti. CR Submanifolds of Kaehlerian and Sasakian Manifolds. Authors (view affiliations) Search within book.

Front Matter. Pages i-x. PDF. Structures on Riemannian Manifolds. Kentaro Yano, Masahiro Kon. Pages Submanifolds. Kentaro Yano, Masahiro Kon. Pages Contact CR Submanifolds. Kentaro Yano, Masahiro Kon. Pages CR. CR-submanifolds of a Kaehler manifold. II Chen, Bang-yen, Journal of Differential Geometry, ; Complex submanifolds of certain non-Kaehler manifolds Kimura, Makoto, Kodai Mathematical Journal, ; Totally umbilical CR-submanifolds of a Kaehler manifold Deshmukh, Sharief and Husain, S.

I., Kodai Mathematical Journal, Cited by: Abstract. Let \(\bar M\) be a complex m-dimensional (real 2m-dimensional) Kaehlerian manifold with almost complex structure J and with Kaehlerian metric g. Let M be a real n-dimensional Riemannian manifold isometrically immersed in \(\bar M\).We denote by the same g the Riemannian metric tensor field induced on M from that of \(\bar M\).The operator of covariant.

In mathematics, a CR manifold is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge. Formally, a CR manifold is a differentiable manifold M together with a preferred complex distribution L, or in other words a complex subbundle of the complexified.

On CR-submanifolds of (H)-paracontact Sasakian manifold Barnali Laha 1 and Arindam Cr Submanifolds of Kaehl.& Sasakian Manifolds book 2 1 Department of Mathematics, Jadavpur University, Kolkata, India 2 Department of Mathematics, Jadavpur University, Kolkata, India Abstract: The object of this paper is to prove some of the properties of (H)-paracontact Sasakian manifold.

[Blair-Chen] D.E. Blair, B.-Y. Chen, On CR-submanifolds of Hermitian manifolds, Israel J. Math. 34 (), –36 3. [Bry ant] R. Bryan t, A n intr o duction to Li e gr oups and symple ctic ge Author: Liviu Ornea.

Book Annex Membership Educators Gift Cards Stores & Events Help. Auto Suggestions are available once you type at least 3 letters. Use up arrow (for mozilla firefox browser alt+up arrow) and down arrow (for mozilla firefox browser alt+down arrow) to Cr Submanifolds of Kaehl.& Sasakian Manifolds book and enter to : $ CR-SUBMANIFOLDS.

A CLASS OF EXAMPLES. 3 If a momentum map exists, one can prove, by just slightly generalizing the symplectic and K ahler situation, the following Proposition Let (M;g;F) be a structured manifold, G a connected group of automor-phisms of the structure.

If an associated momentum map exists for which 0 2 g is a regular. Foliations with bundle-like metric on CR-submanifolds of locally conformal Kähler manifolds. Let (M, g) be a Riemannian manifold and F a foliation on M.

The metric g is said to be bundle-like for the foliation F if the induced metric on the transversal distribution D ⊥ is parallel with respect to the intrinsic connection on D ⊥.Cited by: 7. CR-submanifolds of Kaehler manifolds and also studied generalised CR-submanifolds of Sasakian manifolds [2].

InOubina [3] introduced a new class of almost contact Riemannian manifolds knows as trans-Sasakian manifolds. After M.

Shahid studied CR-submanifolds of trans-Sasakian manifold [4] and generic submanifolds of trans-Sasakian. CR-Submanifolds of an (epsilon)-Paracontact Sasakian Manifold In this section we ﬁrst deﬁne D -totally geodesic(resp.

D ⊥ - totally geodesic) and then D -umbilic(resp. D ⊥ - umbilic). Buy Geometry of CR-Submanifolds (Mathematics and its Applications) on FREE SHIPPING on qualified ordersCited by: In this paper we study CR-submanifolds of (𝜖)-Lorentzian Para-sasakian manifold endowed with quarter symmetric non-metric connection which include the usual LP-sasakian manifold.

Let ∇ be a linear connection in n Where 𝜂 is 1-form. B.Y. Chen studied warped product CR-submanifolds in Kaehler manifolds and introduced the notion of CR-warped product [4]. Later I. Hasegawa and I. Mihai studied contact CR-warped product submanifolds in Sasakian man-ifolds [6].

In this paper we study warped product contact CR-submanifolds of trans-Sasakian manifolds which is more general than [6]. J: H!H. We refer to such manifolds simply as CR manifolds.

A CR mapping between two CR manifolds is a smooth mapping whose tangent map restricts to a complex linear bundle map between the respective contact distributions.

A CR embedding is a CR mapping whichisalsoanembedding. Typically in studying CR embeddings one works with an arbitrary. CR-Warped Product Submanifolds of Lorentzian Manifolds where ∇ is the Levi-Civita connection on M.

Let M = N 1 × f N 2 be a warped product manifold, this means that N 1 is totally geodesic and N 2 is totally umbilical submanifold of M, respectively. The notion of CR-submanifolds of Kaehler manifolds was introduced byFile Size: KB. Finally, certain parallel operators on submanifolds are investigated.

Key words: Almost paracontact metric manifold, para-Sasakian manifold, ˘?-submanifold, almost semiinvariant ˘-submanifolds, para-CR-structure. Introduction The theory of almost paracontact structures on Riemannian manifolds was introduced by Sato [11, 12]. Since. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR : Springer Singapore.

CONTACT CR-SUBMANIFOLDS OF SASAKIAN MANIFOLDS Cz Vz+ (z,). Since the vector field Z is an element of D Zis in TiM. Thus we have from the above equation VZ 0, that is, the vector field is parallel along any vector field in D 4.

SOME COVARIANT DIFFERENTIATIONS. DEFINITION In a contact CR-submanifold M of a Sasakian manifold M, we define. 4 Semi-invariant submanifolds in almost contact metric manifolds 5 Contact CR-products in Sasakian manifolds Contact CR-products Contact CR warped products Contact CR-warped products in Kenmotsu manifolds CR doubly warped products in trans-Sasakian manifolds Marian Ioan MUNTEANU (UAIC) The geometry of CR-submanifolds Luxembourg, March 2 / Abstract.

We study submersion of CR-submanifolds of an l.c.q.K. manifold. We have shown that if an almost Hermitian manifold admits a Riemannian submersion of a CR-submanifold of a locally conformal quaternion Kaehler manifold, then is a locally conformal quaternion Kaehler manifold.

Introduction. The concept of locally conformal Kaehler manifolds was introduced by Author: Majid Ali Choudhary, Mahmood Jaafari Matehkolaee, Mohd. Jamali. The objective of this paper is to introduce the notion of slant submanifolds of an indeﬁnite Sasakian manifolds. We study the existence problem and establish an interplay between slant lightlike submanifolds and contact Cauchy Riemann (CR)-lightlike submanifolds [10].

The concept of a CR-manifold (CR-structure) has been defined having in mind the geometric structure induced on a real hypersurface of. Let be a real differentiable manifold and the tangent bundle of. One says that is a CR-manifold if there exists a complex subbundle of the complexified tangent bundle satisfying the conditions:.

Recently, Hasegawa and Mihai proved that warped product of the type in Sasakian manifolds is trivial where and are invariant and anti-invariant submanifolds of a Sasakian manifold, respectively.

In this paper we study warped product submanifolds of a Sasakian by: 4. CR-submanifolds of a Lorentzian para-Sasakian manifold Proposition Let M be a ξ−vertical CR-submanifold of a Lorentzian para- Sasakian manifold M with semi-symmetric non-metric connection.

Then the distribution D⊥ is parallel with respect to the connection ∇ on M, if and only if, A X ∈D⊥ N for each X ∈D⊥ and N∈TM⊥. Proof: Let.Y,X ∈D⊥ Then using ().

Submersion of Semi-invariant Submanifolds of Contact Manifolds. Vibha Srivastava1 and Department of Mathematics, University of Allahabad, Allahabad, Uttar Pradesh, India. Abstract. In this paper, we discuss submersion of semi-invariant submanifolds of contact manifolds and derive some results on its geometry.

We also derive. Reduction in codimension of mixed foliate CR-submanifolds of a Kaehler manifold Deshmukh, Sharief, Kodai Mathematical Journal, ; Hemi-Slant Warped Product Submanifolds of Nearly Kaehler Manifolds Al-Solamy, Falleh R.

and Khan, Meraj Ali, Abstract and Applied Analysis, Cited by: Abstract: We develop a complete local theory for CR embedded submanifolds of CR manifolds in a way which parallels the Ricci calculus for Riemannian submanifold theory.

In particular, we establish the subtle relationship between the submanifold and ambient standard tractor bundles, allowing us to relate the respective normal Cartan (or tractor) connections via. Generalized CR (GCR)-lightlike submanifolds of indefinite almost contact manifolds were introduced by K.

Duggal and B. Sahin, with the assumption that they are tangent to the structure vector field ξ of the almost contact structure (φ,η,ξ).Author: Samuel. Ssekajja. On Invariant Submanifolds of LP-Sasakian Manifolds Avijit Sarkar, Matilal Sen Department of Mathematics, University of Burdwan, Golapbag, BurdwanWest Bengal, India, [email protected] Presented by Oscar Garc´ıa Prada Received March 2, Abstract: The object of the present paper is to ﬁnd a necessary and suﬃcient condition for.

manifolds we can ﬁnd in the recent literature: paraquaternionic submanifolds [31], Kahler and para-Ka¨hler submanifolds [2, 27], normal semi-invariant submanifolds [1, 8], lightlike submanifolds [19, 20], F-invariant submanifolds [32]. In this note we deﬁne a new class of submanifolds of paraquaternionic Kahler manifolds, which we call.

Abstract. The differential geometry of CR submanifolds of a Kaehler manifold is studied. Theorems about totally geodesic CR submanifolds and totally umbilical CR submanifolds are given. Introduction. Many papers have been concerned with complex submani-folds of complex manifolds, especially of complex space forms (see [4] for a survey of.

CHAPTER IV: CR-SUBMANIFOLDS OF NEARLY KAHELER MANIFOLDS Introduction Some Integrability conditions for the distributions on CR-submanifolds of nearly Kaehler manifold Totally umbilical CR-submanifolds of a nearly Kaehler manifold.

CHAPTER V: CR-SUBMANIFOLDS AND ALMOST CONTACT STRUCTURE Introduction CR. Geometry of Submanifolds Volume 22 of Lecture notes in pure and applied mathematics Volume 22 of Monographs and textbooks in pure and applied mathematics Volume 22 of Pure and Applied Mathematics - Marcel Dekker, ISSN Volume 22 of Pure and applied mathematics: a series of monographs and textbooks.

Thus motivated sufficiently, we study Ricci curvature and scalar curvature of submanifolds in contact metric manifolds.

To be more specific, the results obtained (in this paper) for submanifolds of ([kappa], [mu])-space forms generalize the corresponding results for submanifolds of Sasakian space forms and at the same time several results and examples.

An immersed submanifold of a manifold M is the image S of an immersion map f: N → M; in general this image will not be a submanifold as a subset, and an immersion map need not even be injective (one-to-one) – it can have self-intersections.

More narrowly, one can require that the map f: N → M be an injection (one-to-one), in which we call it an injective immersion, and.

On semi-invariant submanifolds of a nearly Sasakian manifold and Weingarten formulas for M is given by XN = −A NX +aφX +∇⊥ X N() where a = η(N) is a function on M, for X,Y ∈ TM,N∈ T⊥M,h(resp. A N) is the second fundamental form (resp. tensor) of M in M¯ and ∇⊥ denotes the operator of the normal connection.

Legendrian minimal submanifolds in Sasakian manifolds Toru Kajigaya Tohoku University Janu Toru Kajigaya (Tohoku University) Second variation formula and the stabilities of Legendrian minimal submanifolds in Sasakian manifoldsJanu 1 / File Size: KB. Submanifolds of a Lorentzian Para-Sasakian Manifold A submanifold M of an LP-Sasakian manifold M¯ is said to be semi-invariant submanifold [8] if the following conditions are satisﬁed (i) TM = D⊕D⊥⊕{ξ}, where D, D⊥ are orthogonal diﬀerentiable distributions on M and {ξ} is the 1-dimensional distribution spanned by ξ.A.

Sarkar and M. Sen: On invariant submanifolds of trans-Sasakian manifolds 31 for all vector ﬁelds X;Y tangent to M and normal vector ﬁeld N on M;where Ñ is the Riemannian connection on M deﬁned by the induced metric g and Ñ? is the normal connection on T?M of M; h is the second fundamental form of the immersion.

A submanifold M of M˜ is said to be invariant if the Cited by: 4.hypersurfaces or CR manifolds of higher codimension. The investigation of such properties for Levi-degenerate sub-manifolds was ﬁrst carried out in the recent work of Baouendi, Ebenfelt, Rothschild [1] and in the subsequent works [14,2].

For a certain class of Levi-degenerate real-analytic generic submanifolds of CN, it was shown in [1,14,2] that.