Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications

ISBN-13: 9789048146789 / Angielski / Miękka / 2010 / 303 str.

Krishan L. Duggal; PhD Aurel Bejancu

Opis

This book has been written with a two-fold approach in mind: firstly, it adds to the theory of submanifolds the missing part of lightlike (degenerate) submanifolds of semi-Riemannian manifolds, and, secondly, it applies relevant mathematical results to branches of physics. It is the first-ever attempt in mathematical literature to present the most important results on null curves, lightlike hypersurfaces and their applications to relativistic electromagnetism, radiation fields, Killing horizons and asymptotically flat spacetimes in a consistent way. Many striking differences between non-degenerate and degenerate geometry are highlighted, and open problems for both mathematicians and physicists are given. Audience: This book will be of interest to graduate students, research assistants and faculty working in differential geometry and mathematical physics.

Spis treści

Preface. 1. Algebraic Preliminaries. 2. Differential-Geometric Structures on Manifolds. 3. Geometry of Null Curves in Lorentz Manifolds. 4. Lightlike Hypersurfaces of Semi-Riemannian Manifolds. 5. Lightlike Submanifolds of Semi-Riemannian Manifolds. 6. CR-Lightlike Submanifolds of Indefinite Kaehler Manifolds. 7. Lightlike Hypersurfaces of Lorentz Framed Manifolds. 8. Lightlike Hypersurfaces and Electromagnetism. 9. Lightlike Hypersurfaces and General Relativity. References. Author Index. Subject Index.