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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 1999, Volume 6, Number 1/2, Pages 10–21
(Mi jmag399)
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This article is cited in 1 scientific paper (total in 1 paper)
Strongly parabolic timelike submanifolds of Minkowsky space
A. Borisenkoa, M. L. Rabelob, K. Tenenblatb a Department of Mathematics and Mechanics Faculty, Kharkov National University, 4 Svobody Sq., 31077, Kharkov, Ukraine
b Depertamento de Matemática Universidade de Brasília, 71910-900 Brasília, DF, Brasil
Abstract:
R. P. Newman proved that a timelike geodesically complete pseudo-Riemannian manifold with nonnegative Ricci curvature for all vectors and admites a timelike line is isometric to the product of that line and a spacelike complete Riemannian manifold. This result gave a complete proof of a conjecture of Yau. In this paper we proof a cylinder type-theorem which corresponds to the extrinsic version of Newman's result. Moreover, we show that $k$-strongly parabolic geodesically complete submanifolds of a pseudo-Euclidean space with nonnegative Ricci curvature in the spacelike directions are also cylinders with $k$-dimensional generators.
Received: 29.12.1997
Citation:
A. Borisenko, M. L. Rabelo, K. Tenenblat, “Strongly parabolic timelike submanifolds of Minkowsky space”, Mat. Fiz. Anal. Geom., 6:1/2 (1999), 10–21
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https://www.mathnet.ru/eng/jmag399 https://www.mathnet.ru/eng/jmag/v6/i1/p10
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