A major flaw in semi-Riemannian geometry is a shortage of suitable
types of maps between semi-Riemannian manifolds that will compare
their geometric properties. Here, a class of such maps called
semi-Riemannian maps is introduced. The main purpose of this book
is to present results in semi-Riemannian geometry obtained by the
existence of such a map between semi-Riemannian manifolds, as well
as to encourage the reader to explore these maps. The first three
chapters are devoted to the development of fundamental concepts and
formulas in semi-Riemannian geometry which are used throughout the
work. In Chapters 4 and 5 semi-Riemannian maps and such maps with
respect to a semi-Riemannian foliation are studied. Chapter 6
studies the maps from a semi-Riemannian manifold to 1-dimensional
semi- Euclidean space. In Chapter 7 some splitting theorems are
obtained by using the existence of a semi-Riemannian map. Audience:
This volume will be of interest to mathematicians and physicists
whose work involves differential geometry, global analysis, or
relativity and gravitation.
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