%0 Book Section
%T On the conformal geometry of transverse Riemann-Lorentz manifolds.
publisher Real Sociedad Matemática Española
%D 2007
%U 978-84-935193-1-2
%@ https://hdl.handle.net/20.500.14352/53205
%X 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
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