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Null curves and hypersurfaces of semi-Riemannian manifolds. (English) Zbl 1144.53002

Hackensack, NJ: World Scientific (ISBN 978-981-270-647-8/hbk). viii, 293 p. (2007).
The objective of this book is to present a comprehensive up to date information on the differential geometry of null curves and light-like hypersurfaces. The motivation comes from considerable new information on the geometry of these two interrelated topics and their use in mathematical physics. Moreover, these topics are suitable for graduate students who know the theory of nonnull curves and surfaces and are interested in their null counterparts. There does not exist any other text book covering the material included in this book which is just within the understanding (neither too high nor too elementary) of a graduate student. A senior level undergraduate course in differential geometry is the sole prerequisite.
This book has the following special features:
The preliminaries are introduced as needed at the appropriate places. We expect that this approach will help the readers to understand each chapter independently without knowing all the prerequisites in the beginning.
This is the first-ever graduate text book on null curves and hypersurfaces.
The book contains a large variety of solved examples and exercises which range from elementary to higher levels.
The sequence of chapters is arranged so that the understanding of a chapter stimulates interest in reading the next one and so on.

MSC:

53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C40 Global submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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