Eduardo García-Río, D. N. Kupeli

Semi-Riemannian Maps and Their Applications (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 198
• Erscheinungstermin: 29. Juni 2013
• Englisch
• ISBN-13: 9789401729796
• Artikelnr.: 44172593

Inhaltsangabe

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.