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On the conformal geometry of transverse Riemann-Lorentz manifolds.

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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
Subjects:Sciences > Mathematics > Differential geometry
ID Code:20276
Deposited On:06 Mar 2013 15:01
Last Modified:12 Dec 2018 15:13

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