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＜E-Book＞
Semi-Riemannian Maps and Their Applications / by Eduardo García-Río, D.N. Kupeli
(Mathematics and Its Applications ; 475)

Edition	1st ed. 1999.
Publisher	(Dordrecht : Springer Netherlands : Imprint: Springer)
Year	1999
Language	English
Size	X, 198 p : online resource
Authors	*García-Río, Eduardo author Kupeli, D.N author SpringerLink (Online service)
Subjects	LCSH:Geometry, Differential LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Mathematical physics FREE:Differential Geometry FREE:Global Analysis and Analysis on Manifolds FREE:Theoretical, Mathematical and Computational Physics
Notes	1 Linear Algebra of Indefinite Inner Product Spaces -- 2 Semi-Riemannian Manifolds -- 3 Second Fundamental Form of a Map -- 4 Semi-Riemannian Maps -- 5 Semi-Riemannian Transversal Maps -- 6 Semi-Riemannian Eikonal Equations and The Semi-Riemannian Regular Interval Theorem -- 7 Applications To Splitting Theorems -- A Submanifolds of Semi-Riemannian Manifolds -- A.1 Semi-Riemannian Submanifolds -- A.2 Degenerate Submanifolds -- B Riemannian and Lorentzian Geometry -- B.1 Riemannian Geometry -- B.2 Lorentzian Geometry 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 HTTP:URL=https://doi.org/10.1007/978-94-017-2979-6

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