scholarly journals Submanifolds of Sasakian Manifolds with Certain Parallel Operators

ISRN Geometry ◽  
2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Amira A. Ishan
Keyword(s):  
Tensor Field ◽  
Sasakian Manifold ◽  
Symmetric Tensor ◽  
Sasakian Manifolds ◽  
Invariant Submanifold

We study submanifolds of Sasakian manifolds and obtain a condition under which certain naturally defined symmetric tensor field on the submanifold is to be parallel and use this result to obtain conditions under which a submanifold of the Sasakian manifold is an invariant submanifold.

A note on slant submanifolds of nearly trans-Sasakian manifolds

2010 ◽  
Vol 60 (1) ◽  
Author(s):  
Falleh Al-Solamy ◽  
Viqar Khan
Keyword(s):  
Tensor Field ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Slant Submanifolds

AbstractThe geometry of slant submanifolds of a nearly trans-Sasakian manifold is studied when the tensor field Q is parallel. It is proved that Q is not parallel on the submanifold unless it is anti-invariant and thus the result of [CABRERIZO, J. L.—CARRIAZO, A.—FERNANDEZ, L. M.—FERNANDEZ, M.: Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), 125–138] and [GUPTA, R. S.—KHURSHEED HAIDER, S. M.—SHARFUDIN, A.: Slant submanifolds of a trans-Sasakian manifold, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 47 (2004), 45–57] are generalized.

scholarly journals On the topology of Sasakian manifolds

2003 ◽  
Vol 93 (1) ◽  
pp. 99 ◽  
Author(s):  
Gheorghe Pitiş
Keyword(s):  
Vector Field ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Bisectional Curvature

The notion of $q$-bisectional curvature of a Sasakian manifold $M$ is defined. It is proved that if $M$ has lower bounded $q$-bisectional curvature and contains a compact invariant submanifold tangent to the structure vector field then $M$ is compact. Myers and Frankel type theorems for Sasakian manifolds with lower bounded and positive $q$-bisectional curvature, respectively, are also given.

A new method for inextensible flows of timelike curves in 4-dimensional LP-Sasakian manifolds

2015 ◽  
Vol 08 (04) ◽  
pp. 1550073 ◽  
Author(s):  
Talat Körpinar
Keyword(s):  
Tensor Field ◽  
Sasakian Manifold ◽  
New Method ◽  
Conformally Flat ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
Practical Applications ◽  
Inextensible Flows ◽  
Necessary And Sufficient ◽  
The Given

Inextensible flows of timelike curves plays an important role in practical applications. In this paper, we construct a new method for inextensible flows of timelike curves in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional LP-Sasakian manifold. With this new representation, we derive the necessary and sufficient condition for the given curve to be the inextensible flow. By using curvature tensor field, we give some characterizations for curvatures of a timelike curve in a conformally flat, quasi conformally flat and conformally symmetric 4-dimensional LP-Sasakian manifold. Finally, we obtain flows of some associated curves of timelike curves.

scholarly journals Skew semi-invariant submanifolds of generalized quasi-Sasakian manifolds

2018 ◽  
Vol 9 (2) ◽  
pp. 188-197 ◽  
Author(s):  
M.D. Siddiqi ◽  
A. Haseeb ◽  
M. Ahmad
Keyword(s):  
Sasakian Manifold ◽  
Equivalence Relations ◽  
Cr Manifold ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Contact Metric Manifold ◽  
Almost Contact Metric Manifold ◽  
New Class ◽  
Almost Contact Metric ◽  
Invariant Submanifolds

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 mixed totally geodesic. Also it is shown that a  skew semi-invariant submanifold of a generalized Quasi-Sasakian manifold will be anti-invariant if and only if $A_{\xi}=0$; and the submanifold will be skew semi-invariant submanifold if $\nabla w=0$. The equivalence relations for the  skew semi-invariant submanifold of a  generalized Quasi-Sasakian manifold are given. Furthermore, we have proved that a skew semi-invariant $\xi^\perp$-submanifold of a normal almost contact metric manifold and a generalized Quasi-Sasakian manifold with non-trivial invariant distribution is $CR$-manifold. An example of dimension 5 is given to show that a skew semi-invariant $\xi^\perp$ submanifold is a $CR$-structure on the manifold.

scholarly journals ON AN INVARIANT SUBMANIFOLD OF HYPERBOLIC SASAKIAN MANIFOLDS

2017 ◽  
pp. 353
Author(s):  
Shravan Kumar Pandey ◽  
Ram Nawal Singh
Keyword(s):  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Totally Geodesic ◽  
Invariant Submanifolds

The object of the present paper is to study an invariant submanifold of hyperbolic Sasakian maifolds. In this paper, we consider semiparallel and 2-semiparallel invariant submanifolds of hyperbolic Sasakian manifold and it is shown that these submanifolds are totally geodesic. It is also proved that on an invariant submanifold of hyperbolic Sasakian manifolds the conditions $I(X, Y).\alpha = 0$, $I(X, Y).\tilde{\nabla}\alpha = 0$, $C(X, Y).\alpha = 0$, $C(X, Y).\tilde{nabla}\alpha = 0$ holds if and only if it is totally geodesic.

scholarly journals On some classes of invariant submanifolds of lorentzian para-sasakian manifolds

2016 ◽  
Vol 47 (2) ◽  
pp. 207-220
Author(s):  
Srimayee Samui ◽  
Uday Chand De
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Invariant Submanifolds ◽  
Concircular Curvature Tensor

The object of the present paper is to study invariant submanifolds of Lorenzian Para-Sasakian manifolds. We consider the recurrent and bi-recurrent invariant submanifolds of Lorentzian para-Sasakian manifolds and pseudo-parallel and generalized Ricci pseudo-parallel invariant submanifolds of Lorentzian para-Sasakian manifolds. Also we search for the conditions $\mathcal{Z}(X,Y)\cdot\alpha=fQ(g,\alpha)$ and $\mathcal{Z}(X,Y)\cdot\alpha=fQ(S,\alpha)$ on invariant submanifolds of Lorentzian para-Sasakian manifolds, where $\mathcal{Z}$ is the concircular curvature tensor. Finally, we construct an example of an invariant submanifold of Lorentzian para Sasakian manifold.

scholarly journals On Totally Contact Umbilical Contact CR-Lightlike Submanifolds Of Indefinite Sasakian Manifolds

2014 ◽  
Vol 47 (1) ◽  
Author(s):  
Manish Gogna ◽  
Rakesh Kumar ◽  
R. K. Nagaich
Keyword(s):  
Sasakian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
Invariant Submanifold ◽  
Necessary And Sufficient ◽  
Lightlike Submanifolds ◽  
Lightlike Submanifold

AbstractAfter brief introduction, we prove that a totally contact umbilical CR- lightlike submanifold is totally contact geodesic. We obtain a necessary and sufficient condition for a CR-lightlike submanifold to be an anti-invariant submanifold. Finally, we characterize a contact CR-lightlike submanifold of indefinite Sasakian manifold to be a contact CR-lightlike product

scholarly journals Three-dimensional trans-Sasakian manifolds and solitons

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sudhakar Kumar Chaubey ◽  
Uday Chand De
Keyword(s):  
Design Methodology ◽  
Three Dimensional ◽  
Sasakian Manifold ◽  
Symmetric Tensor ◽  
Riemannian Metric ◽  
Ricci Solitons ◽  
Sasakian Manifolds ◽  
Constant Multiple ◽  
Content Type ◽  
Order Parallel

PurposeThe authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the Ricci solitons, η-Ricci solitons and three-dimensional weakly  symmetric trans-Sasakian manifolds. Finally, they give a nontrivial example of three-dimensional proper trans-Sasakian manifold.Design/methodology/approachThe authors have used the tensorial approach to achieve the goal.FindingsA second-order parallel symmetric tensor on a three-dimensional trans-Sasakian manifold is a constant multiple of the associated Riemannian metric g.Originality/valueThe authors declare that the manuscript is original and it has not been submitted to any other journal for possible publication.

Some Properties of Para-Sasakian Manifolds

2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Sasakian Manifold ◽  
Subject Classification ◽  
Killing Vector Field ◽  
Sasakian Manifolds ◽  
Geometric Properties ◽  
Paper Author

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

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