The self-shrinker in warped product space and the weighted Minkowski inequality

2016 ◽  
Vol 145 (4) ◽  
pp. 1763-1772
Author(s):  
Guoqiang Wu
Keyword(s):  
Product Space ◽  
Warped Product ◽  
Minkowski Inequality ◽  
The Self

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 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

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.

scholarly journals Classification of Einstein equations with cosmological constant in warped product space-time

2018 ◽  
Vol 15 (03) ◽  
pp. 1850041 ◽  
Author(s):  
F. Gholami ◽  
A. Haji-Badali ◽  
F. Darabi
Keyword(s):  
Cosmological Constant ◽  
Product Space ◽  
Warped Product ◽  
Space Time ◽  
Einstein Equations ◽  
Twisted Product ◽  
Product Structures ◽  
Static Space

We classify all warped product space-times in three categories as (i) generalized twisted product structures, (ii) base conformal warped product structures and (iii) generalized static space-times and then we obtain the Einstein equations with the corresponding cosmological constant by which we can determine uniquely the warp functions in these warped product space-times.

The symmetry of warped product space-times

1991 ◽  
Vol 23 (6) ◽  
pp. 671-681 ◽  
Author(s):  
R. Deszcz ◽  
L. Verstraelen ◽  
L. Vrancken
Keyword(s):  
Product Space ◽  
Warped Product
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