On the conformal geometry of transverse Riemann-Lorentz manifolds.

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