Differential Geometry of Lightlike Submanifolds [Paperback]

This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite K?hlerian, Sasakian and quaternion K?hler manifolds.

Preface.- Notations.- 1 Preliminaries.- 2 Lightlike hypersurfaces.- 3 Applications of lightlike hypersurfaces.- 4 Half-lightlike submanifolds.- 5 Lightlike submanifolds.- 6 Submanifolds of indefinite K?hler manifolds.- 7 Submanifolds of indefinite Sasakian manifolds.- 8 Submanifolds of Indefinite quaternion K?hler manifolds.- 9 Applications of lightlike geometry.- Bibliography.- Index.

From the reviews:

It provides a reasonably self-contained and very comprehensive account of all aspects of the subject. & The book contains more than 400 references to the literature, as well as a wealth of applications to physics (general relativity). Written by two of the main contributors to the field this comprehensive presentation is certain to be the standard work for the foreseeable future. (M. Kunzinger, Monatshefte f?r Mathematik, Vol. 167 (1), July, 2012)

This is the first systematic account of the main results in the theory of lightlike submanifolds of semi-Riemannian manifolds which have a geometric structure, such as almost Hermitian, almost contact metric or quaternion K?hler. Using these structures, the book presents interesting classes of submanifolds whose geometry is very rich.

The book also includes hypersurfaces of semi-Riemannian manifolds, their use in general relativity and Osserman geometry, half-lightlike submanifolds of semi-Riemannian manifolds, lightlike submersions, screen conformal submersions, and their applications in harmonic maps.

Basic constructions and definitions are presented as preliminary background in every chapter. The presentation explores applications and suggests several open questions.

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