scholarly journals WARPED EMBEDDINGS BETWEEN EINSTEIN MANIFOLDS

2010 ◽  
Vol 25 (18) ◽  
pp. 1521-1530 ◽  
Author(s):  
HUAN-XIONG YANG ◽  
LIU ZHAO
Keyword(s):  
Einstein Manifold ◽  
Explicit Solutions ◽  
Einstein Manifolds ◽  
Higher Dimensional ◽  
Potential Applications ◽  
Lower Dimensional

Warped embeddings from a lower dimensional Einstein manifold into a higher dimensional one are analyzed. Explicit solutions for the embedding metrics are obtained for all cases of codimension 1 embeddings and some of the codimension n>1 cases. Some of the interesting features of the embedding metrics are pointed out and potential applications of the embeddings are discussed.

ON FORMULATIONS AND SOLUTIONS OF SIMPLEX EQUATIONS

1996 ◽  
Vol 11 (24) ◽  
pp. 4453-4463 ◽  
Author(s):  
J. SCOTT CARTER ◽  
MASAHICO SAITO
Keyword(s):  
Higher Dimensional ◽  
Lower Dimensional

A version of the tetrahedral equation is formulated using a pictorial interpretation of the Frenkel-Moore equation. The picture gives a solution that is a product of quantum Yang-Baxter solutions. Higher-dimensional variants of the Frenkel-Moore equations are found from this pictorial interpretation, and the pictures reduce their solvability to the solvability of lower-dimensional equations.

scholarly journals Stability of Riemannian manifolds with Killing spinors

2017 ◽  
Vol 28 (01) ◽  
pp. 1750005 ◽  
Author(s):  
Changliang Wang
Keyword(s):  
Riemannian Manifolds ◽  
Einstein Manifold ◽  
Stability Result ◽  
Warped Products ◽  
Einstein Manifolds ◽  
Killing Spinors ◽  
Parallel Spinors ◽  
Unstable Manifolds ◽  
The Stability ◽  
Complete Riemannian Manifolds

Riemannian manifolds with nonzero Killing spinors are Einstein manifolds. Kröncke proved that all complete Riemannian manifolds with imaginary Killing spinors are (linearly) strictly stable in [Stable and unstable Einstein warped products, preprint (2015), arXiv:1507.01782v1 ]. In this paper, we obtain a new proof for this stability result by using a Bochner-type formula in [X. Dai, X. Wang and G. Wei, On the stability of Riemannian manifold with parallel spinors, Invent. Math. 161(1) (2005) 151–176; M. Wang, Preserving parallel spinors under metric deformations, Indiana Univ. Math. J. 40 (1991) 815–844]. Moreover, existence of real Killing spinors is closely related to the Sasaki–Einstein structure. A regular Sasaki–Einstein manifold is essentially the total space of a certain principal [Formula: see text]-bundle over a Kähler–Einstein manifold. We prove that if the base space is a product of two Kähler–Einstein manifolds then the regular Sasaki–Einstein manifold is unstable. This provides us many new examples of unstable manifolds with real Killing spinors.

scholarly journals On some classes of mixed-super quasi-Einstein manifolds

2016 ◽  
Vol 8 (1) ◽  
pp. 32-52
Author(s):  
Santu Dey ◽  
Buddhadev Pal ◽  
Arindam Bhattacharyya
Keyword(s):  
Warped Product ◽  
Einstein Manifold ◽  
Warped Products ◽  
Einstein Manifolds

Abstract Quasi-Einstein manifold and generalized quasi-Einstein manifold are the generalizations of Einstein manifold. The purpose of this paper is to study the mixed super quasi-Einstein manifold which is also the generalizations of Einstein manifold satisfying some curvature conditions. We define both Riemannian and Lorentzian doubly warped product on this manifold. Finally, we study the completeness properties of doubly warped products on MS(QE)4 for both the Riemannian and Lorentzian cases.

SOME NONCONFORMAL ACCELERATING PERFECT FLUID PLATES OF EMBEDDING CLASS 1 USING SIMILARITY TRANSFORMATIONS

2010 ◽  
Vol 25 (09) ◽  
pp. 1863-1879 ◽  
Author(s):  
Y. K. GUPTA ◽  
PRATIBHA ◽  
SACHIN KUMAR
Keyword(s):  
Perfect Fluid ◽  
Flat Space ◽  
Space Time ◽  
Explicit Solutions ◽  
Field Equations ◽  
Similarity Transformations ◽  
Higher Dimensional ◽  
Class 1 ◽  
Brane Theory ◽  
Respective Category

In view of renewed interest in the space–time embedded in higher-dimensional flat space which are useful in extrinsic gravity, string and brane theory, a set of six explicit solutions to Einstein's field equations for nonconformally flat accelerating and shearing perfect fluid plates is obtained using similarity transformations method by considering a five-dimensional flat metric. All the solutions thus obtained are analyzed physically. All the solutions are new in their respective category as far as authors are aware.

scholarly journals Bochner-type Formulas for the Weyl Tensor on Four-dimensional Einstein Manifolds

2018 ◽  
Vol 2020 (12) ◽  
pp. 3794-3823
Author(s):  
Giovanni Catino ◽  
Paolo Mastrolia
Keyword(s):  
Covariant Derivative ◽  
Weyl Tensor ◽  
Einstein Manifold ◽  
Higher Order ◽  
Einstein Metric ◽  
Einstein Manifolds ◽  
Rigidity Result ◽  
Type Formula ◽  
Definition Of ◽  
Integral Identities

Abstract The very definition of an Einstein metric implies that all its geometry is encoded in the Weyl tensor. With this in mind, in this paper we derive higher-order Bochner-type formulas for the Weyl tensor on a four-dimensional Einstein manifold. In particular, we prove a 2nd Bochner-type formula that, formally, extends to the covariant derivative level the classical one for the Weyl tensor obtained by Derdziński in 1983. As a consequence, we deduce new integral identities involving the Weyl tensor and its derivatives on a compact four-dimensional Einstein manifold and we derive a new rigidity result.

Mixed Norm Type Hardy Inequalities

2011 ◽  
Vol 54 (4) ◽  
pp. 630-644 ◽  
Author(s):  
Alberto Fiorenza ◽  
Babita Gupta ◽  
Pankaj Jain
Keyword(s):  
Integral Operators ◽  
Mixed Norm ◽  
Hardy Inequalities ◽  
Higher Dimensional ◽  
Lower Dimensional

AbstractHigher dimensional mixed norm type inequalities involving certain integral operators are characterized in terms of the corresponding lower dimensional inequalities.

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