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 Some Conditions on Trans-Sasakian Manifolds to Be Homothetic to Sasakian Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1887
Author(s):  
Sharief Deshmukh ◽  
Amira Ishan ◽  
Olga Belova ◽  
Suha B. Al-Shaikh
Keyword(s):  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
3 Dimensional ◽  
Necessary And Sufficient ◽  
Simply Connected

In this paper, we study 3-dimensional compact and connected trans-Sasakian manifolds and find necessary and sufficient conditions under which these manifolds are homothetic to Sasakian manifolds. First, four results in this paper deal with finding necessary and sufficient conditions on a compact and connected trans-Sasakian manifold to be homothetic to a compact and connected Sasakian manifold, and the fifth result deals with finding necessary and sufficient condition on a connected trans-Sasakian manifold to be homothetic to a connected Sasakian manifold. Finally, we find necessary and sufficient conditions on a compact and simply connected trans-Sasakian manifold to be homothetic to a compact and simply connected Einstein 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 Two theorems on(ϵ)-Sasakian manifolds

1998 ◽  
Vol 21 (2) ◽  
pp. 249-254 ◽  
Author(s):  
Xu Xufeng ◽  
Chao Xiaoli
Keyword(s):  
Riemannian Manifold ◽  
Sasakian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
Necessary And Sufficient ◽  
Kaehlerian Manifold

In this paper, We prove that every(ϵ)-sasakian manifold is a hypersurface of an indefinite kaehlerian manifold, and give a necessary and sufficient condition for a Riemannian manifold to be an(ϵ)-sasakian manifold.

scholarly journals Bipartite graphs with close domination and k-domination numbers

2020 ◽  
Vol 18 (1) ◽  
pp. 873-885
Author(s):  
Gülnaz Boruzanlı Ekinci ◽  
Csilla Bujtás
Keyword(s):  
Positive Integer ◽  
Dominating Set ◽  
Domination Number ◽  
Bipartite Graphs ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Minimum Cardinality ◽  
Vertex Set ◽  
Necessary And Sufficient ◽  
The Given

Abstract Let k be a positive integer and let G be a graph with vertex set V(G) . A subset D\subseteq V(G) is a k -dominating set if every vertex outside D is adjacent to at least k vertices in D . The k -domination number {\gamma }_{k}(G) is the minimum cardinality of a k -dominating set in G . For any graph G , we know that {\gamma }_{k}(G)\ge \gamma (G)+k-2 where \text{Δ}(G)\ge k\ge 2 and this bound is sharp for every k\ge 2 . In this paper, we characterize bipartite graphs satisfying the equality for k\ge 3 and present a necessary and sufficient condition for a bipartite graph to satisfy the equality hereditarily when k=3 . We also prove that the problem of deciding whether a graph satisfies the given equality is NP-hard in general.

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 A New Method for Inextensible Flows of Timelike Curves in Minkowski Space-Time E14

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Talat Körpinar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Minkowski Space ◽  
Space Time ◽  
New Method ◽  
Frenet Frame ◽  
Partial Differential ◽  
Minkowski Space Time ◽  
Inextensible Flows ◽  
The Given

We construct a new method for inextensible flows of timelike curves in Minkowski space-time E14. Using the Frenet frame of the given curve, we present partial differential equations. We give some characterizations for curvatures of a timelike curve in Minkowski space-time E14.

scholarly journals Para-CR structures on almost paracontact metric manifolds

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Joanna Wełyczko
Keyword(s):  
Sectional Curvature ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Constant Sectional Curvature ◽  
Conformally Flat ◽  
Cr Manifolds ◽  
Cosymplectic Manifolds ◽  
Cr Structures ◽  
Necessary And Sufficient

AbstractAlmost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and sufficient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost paracontact metric manifolds. Especially, it is shown that normal almost paracontact metric manifolds are para-CR. We establish necessary and sufficient conditions for paracontact metric manifolds as well as for almost para-cosymplectic manifolds to be para-CR. We find also basic curvature identities for para-CR paracontact metric manifolds and study their consequences. Among others, we prove that any para-CR paracontact metric manifold of constant sectional curvature and of dimension greater than 3 must be para-Sasakian and its curvature equal to -1. The last assertion does not hold in dimension 3. We show that a conformally flat para-Sasakian manifold is of constant sectional curvature equal to -1. New classes of examples of para-CR manifolds are established.

scholarly journals On endo curvature tensor of a contact metric manifold

2008 ◽  
Vol 39 (2) ◽  
pp. 177-186
Author(s):  
Mohit Kumar Dwivedi ◽  
Jae-Bok Jun ◽  
Mukut Mani Tripathi
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Sasakian Manifold ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Contact Metric Manifold ◽  
Necessary And Sufficient

We prove that a $ ( k ,\mu ) $-manifold with vanishing Endo curvature tensor is a Sasakian manifold. We find a necessary and sufficient condition for a non-Sasakian $ ( k ,\mu ) $-manifold %$M$ whose Endo curvature tensor $ B^{es} $ satisfies $ B^{es}(\xi ,X) \cdot S=0 $, where $S$ is the Ricci tensor. Using $ {\cal D} $-homothetic deformation we obtain an example of an $ N\left( k\right) $-contact metric manifold on which $ B^{es}(\xi ,X)\cdot S\neq 0 $.

scholarly journals Hemi-slant ξ⊥-Riemannian submersions in contact geometry

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3747-3758
Author(s):  
Ramazan Sari ◽  
Mehmet Akyol
Keyword(s):  
Riemannian Manifolds ◽  
Natural Generalization ◽  
Product Manifold ◽  
Necessary And Sufficient Condition ◽  
Sasakian Manifolds ◽  
Riemannian Submersions ◽  
Space Forms ◽  
Base Manifold ◽  
Sasakian Space Forms ◽  
Necessary And Sufficient

M. A. Akyol and R. Sar? [On semi-slant ??-Riemannian submersions, Mediterr. J. Math. 14(6) (2017) 234.] defined semi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. As a generalization of the above notion and natural generalization of anti-invariant ??-Riemannian submersions, semi-invariant ??-Riemannian submersions and slant submersions, we study hemi-slant ??-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We obtain the geometry of foliations, give some examples and find necessary and sufficient condition for the base manifold to be a locally product manifold. Moreover, we obtain some curvature relations from Sasakian space forms between the total space, the base space and the fibres.

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