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Aguirre Dabán, Eduardo and Fernández Mateos, Víctor and Lafuente López, Javier
(2007)
*On the conformal geometry of transverse Riemann-Lorentz manifolds.*
In
XV International Workshop on Geometry and Physics: Puerto de la Cruz, Tenerife, Canary Islands, Spain : September 11-16, 2006.
Publicaciones de la Real Sociedad Matemática Española
(11).
Real Sociedad Matemática Española, Madrid, pp. 205-211.
ISBN 978-84-935193-1-2

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## Abstract

Let M be a connected manifold and let g be a symmetric covariant tensor field of order 2 on M.

Assume that the set of points where g degenerates is not empty. If U is a coordinate system around p 2 , then g is a transverse type-changing metric at p if dp(det(g)) 6= 0, and (M, g) is called a transverse type-changing pseudo-iemannian manifold if g is transverse type-changing at every point of . The set is a hypersurface of M. Moreover, at every point of there exists a one-dimensional radical, that is, the subspace Radp(M) of TpM, which is g-orthogonal to TpM. The index of g is constant on every connected component M = M r; thus M is a union of connected pseudo-Riemannian manifolds. Locally, separates two pseudo-Riemannian manifolds whose indices differ by one unit. The authors consider the cases where separates a Riemannian part from a Lorentzian one, so-called transverse Riemann-Lorentz manifolds. In this paper, they study the conformal geometry of transverse Riemann-Lorentz manifolds

Item Type: | Book Section |
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Subjects: | Sciences > Mathematics > Differential geometry |

ID Code: | 20276 |

Deposited On: | 06 Mar 2013 15:01 |

Last Modified: | 09 Sep 2020 08:08 |

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