Results 41 to 50 of about 2,551 (283)
Asian Journal of Mathematics, 2015 In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure.
He, Chenxu +2 more
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The geometry of warped product singularities [PDF]
International Journal of Geometric Methods in Modern Physics, 2017 In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the ...
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Affine connections on singular multiply warped products and singular twisted products [PDF]
, 2022 In this paper, we generalize the results in [Y. Wang: Affine connections on singular warped products. Int. J. Geom. Methods Mod. Phys. 18(5), 2150076, (2021).] to singular multiply warped products and singular twisted products. We study singular multiply
Wu, Tong, Liu, Siyao, Wang, Yong
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Killing tensors and warped product [PDF]
Annales Polonici Mathematici, 2000 By a Killing tensor one understands a \((1,1)\)-tensor field \(S\) on a Riemannian manifold \((M,g)\) satisfying the conditions \(\langle SX,Y \rangle =\langle X,S Y\rangle\) and \(\langle\nabla S(X,X),X \rangle=0\), for all \(X\) on \(M\). Considering the eigenvalues and the eigendistributions of \(S\), the author gets close relations between certain ...
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Singularity theorems for warped products and the stability of spatial extra dimensions
Journal of High Energy Physics, 2019 New singularity theorems are derived for generic warped-product spacetimes of any dimension. The main purpose is to analyze the stability of (compact or large) extra dimensions against dynamical perturbations.
Nastassja Cipriani +1 more
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Warped Product Submanifolds of Riemannian Product Manifolds [PDF]
Abstract and Applied Analysis, 2012 We study warped product of the type Nθ×fNT and Nθ×fN⊥, where Nθ, NT, and N⊥ are proper slant, invariant, and anti‐invariant submanifolds, respectively, and we prove some basic results and finally obtain some inequalities for squared norm of second fundamental form.
Al-Solamy, Falleh R., Khan, Meraj Ali
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A Moser-Bernstein problem for Riemannian warped products [PDF]
, 2020 In this work we deal with an elliptic non-linear problem, which arises naturally from Riemannian geometry. This problem has clasically been studied in the the Euclidean $n$-dimensional space and it is known as the Moser-Bernstein problem. Nevertheless we
Albujer, Alma L. +2 more
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A remark on Einstein warped products [PDF]
Pacific Journal of Mathematics, 2011 We prove triviality results for Einstein warped products with non-compact bases. These extend previous work by D.-S. Kim and Y.-H. Kim. The proof, from the viewpoint of "quasi-Einstein manifolds" introduced by J. Case, Y.-S. Shu and G. Wei, rely on maximum principles at infinity and Liouville-type theorems.
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Multiply warped products quasi-Einstein manifolds with quarter-symmetric connection [PDF]
, 2016 In this paper we study warped products and multiply warped products on quasi-Einstein manifolds with a quarter-symmetric connection.
Pahan, Sampa +2 more
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Some results on warped and twisted products [PDF]
, 2021 We give a result for a pseudo-Riemannian manifold to be a warped product.
Tastan, Hakan Mete, Aydin, Sibel Gerdan
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