scholarly journals On Einstein warped product space with respect to semi symmetric metric connection

2021 ◽  
Author(s):  
Buddhadev PAL ◽  
Pankaj KUMAR
Keyword(s):  
Product Space ◽  
Warped Product ◽  
Metric Connection

scholarly journals The W2-curvature tensor on warped product manifolds and applications

2016 ◽  
Vol 13 (07) ◽  
pp. 1650099 ◽  
Author(s):  
Sameh Shenawy ◽  
Bülent Ünal
Keyword(s):  
Curvature Tensor ◽  
Product Space ◽  
Warped Product ◽  
Space Time ◽  
Product Manifold ◽  
Warped Product Manifold ◽  
Static Space

The purpose of this paper is to study the [Formula: see text]-curvature tensor on (singly) warped product manifolds as well as on generalized Robertson–Walker and standard static space-times. Some different expressions of the [Formula: see text]-curvature tensor on a warped product manifold in terms of its relation with [Formula: see text]-curvature tensor on the base and fiber manifolds are obtained. Furthermore, we investigate [Formula: see text]-curvature flat warped product manifolds. Many interesting results describing the geometry of the base and fiber manifolds of a [Formula: see text]-curvature flat warped product manifold are derived. Finally, we study the [Formula: see text]-curvature tensor on generalized Robertson–Walker and standard static space-times; we explore the geometry of the fiber of these warped product space-time models that are [Formula: see text]-curvature flat.

scholarly journals Warped product CR-submanifolds of Sasakian manifolds with respect to certain connections

2019 ◽  
Vol 25 (3) ◽  
pp. 194-202
Author(s):  
Shyamal Kumar Hui ◽  
Joydeb Roy
Keyword(s):  
Warped Product ◽  
Ricci Solitons ◽  
Sasakian Manifolds ◽  
Metric Connection ◽  
Cr Submanifolds

The present paper deals with the study of warped product CR-submanifolds of Sasakian manifolds with respect to semisymmetric metric and semisymmetric non-metric connection. Among others, Ricci solitons of such notions have been investigated.

scholarly journals Einstein doubly warped product manifolds with semi-symmetric metric connection

2020 ◽  
Vol 57 ◽  
pp. 7-24
Author(s):  
Punam Gupta ◽  
Abdoul Salam Diallo
Keyword(s):  
Warped Product ◽  
Sufficient Condition ◽  
Product Manifold ◽  
Necessary And Sufficient Condition ◽  
Class A ◽  
Warped Product Manifold ◽  
Metric Connection ◽  
Necessary And Sufficient

In this paper, we study the doubly warped product manifolds with semi-symmetric metric connection. We derive the curvature formulas for doubly warped product manifold with semi-symmetric metric connection in terms of curvatures of components of doubly warped product manifolds. We also prove the necessary and sufficient condition for a doubly warped product manifold to be a warped product manifold. We obtain some results for an Einstein doubly warped product manifold and Einstein-like doubly warped product manifold of class A with respect to a semi-symmetric metric connection.

scholarly journals Invariants of the Riemann tensor for class B warped product space-times

1998 ◽  
Vol 115 (2-3) ◽  
pp. 381-394 ◽  
Author(s):  
Kevin Santosuosso ◽  
Denis Pollney ◽  
Nicos Pelavas ◽  
Peter Musgrave ◽  
Kayll Lake
Keyword(s):  
Product Space ◽  
Warped Product ◽  
Riemann Tensor ◽  
Class B

Special multiply Einstein warped products with an affine connection

2018 ◽  
Vol 15 (07) ◽  
pp. 1850107
Author(s):  
Dan Dumitru
Keyword(s):  
Warped Product ◽  
Affine Connection ◽  
Open Interval ◽  
Einstein Space ◽  
Warped Products ◽  
Ricci Flat ◽  
Metric Connection

The aim of this paper is to study special multiply Einstein warped products having an affine connection. Let [Formula: see text] be a multiply warped product such that [Formula: see text] is an open interval, [Formula: see text] [Formula: see text] [Formula: see text] [Formula: see text] for every [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] an affine connection on [Formula: see text] We compute the warping functions that make [Formula: see text] an Einstein space in the following cases: (a) [Formula: see text] is a semi-symmetric metric/non-metric connection and all the fibers are Ricci flat. (b) [Formula: see text] is a quarter-symmetric metric/non-metric connection and all the fibers are Ricci flat.

scholarly journals Free elasticae and Willmore tori in warped product spaces

1998 ◽  
Vol 40 (2) ◽  
pp. 265-272 ◽  
Author(s):  
Manuel Barros
Keyword(s):  
Variational Problem ◽  
Critical Points ◽  
Product Space ◽  
Warped Product ◽  
Product Spaces ◽  
De Sitter ◽  
Total Squared Curvature ◽  
Principle Of Symmetric Criticality ◽  
Warped Product Spaces

AbstractWe use the principle of symmetric criticality to connect the Willmore variational problem for surfaces in a warped product space with base a circle, and the free elastica variational problem for curves on its fiber. In addition we obtain a rational oneparameter family of closed helices in the anti De Sitter 3-space which are critical points of the total squared curvature functional. This means they are free elasticae. Also they are spacelike; this allows us to construct a corresponding family of spacelike Willmore tori in a certain kind of spacetime close to the Robertson-Walker spaces.

Compact Einstein multiply warped product space with nonpositive scalar curvature

2019 ◽  
Vol 16 (10) ◽  
pp. 1950162 ◽  
Author(s):  
Buddhadev Pal ◽  
Pankaj Kumar
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Product Space ◽  
Warped Product ◽  
Space Time ◽  
Product Spaces ◽  
Warped Product Spaces ◽  
Friedmann Robertson Walker

In this paper, we characterize the Einstein multiply warped product space with nonpositive scalar curvature. As a result, it is shown that, if [Formula: see text] is Einstein multiple-warped product spaces with compact base and nonpositive scalar curvature, then [Formula: see text] is simply a Riemannian manifold. Next, we apply our result on Generalized Robertson–Walker space-time and Generalized Friedmann–Robertson–Walker space-time.

scholarly journals Gray’s decomposition on doubly warped product manifolds and applications

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3767-3776
Author(s):  
Hoda El-Sayied ◽  
Carlo Mantica ◽  
Sameh Shenawy ◽  
Noha Syied
Keyword(s):  
Covariant Derivative ◽  
Ricci Tensor ◽  
Product Space ◽  
Warped Product ◽  
Necessary Conditions ◽  
Type A ◽  
Product Manifold ◽  
Warped Product Manifold ◽  
Sufficient And Necessary Conditions

A. Gray presented an interesting O(n) invariant decomposition of the covariant derivative of the Ricci tensor. Manifolds whose Ricci tensor satisfies the defining property of each orthogonal class are called Einstein-like manifolds. In the present paper, we answered the following question: Under what condition(s), does a factor manifold Mi,i = 1,2 of a doubly warped product manifold M =f2 M1 x f1 M2 lie in the same Einstein- like class of M? By imposing sufficient and necessary conditions on the warping functions, an inheritance property of each class is proved. As an application, Einstein-like doubly warped product space-times of type A,B or P are considered.

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