Advertisement

Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications

  • Krishan L. Duggal
  • Aurel Bejancu

Part of the Mathematics and Its Applications book series (MAIA, volume 364)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Krishan L. Duggal, Aurel Bejancu
    Pages 1-17
  3. Krishan L. Duggal, Aurel Bejancu
    Pages 18-51
  4. Krishan L. Duggal, Aurel Bejancu
    Pages 52-76
  5. Krishan L. Duggal, Aurel Bejancu
    Pages 77-138
  6. Krishan L. Duggal, Aurel Bejancu
    Pages 139-189
  7. Krishan L. Duggal, Aurel Bejancu
    Pages 190-210
  8. Krishan L. Duggal, Aurel Bejancu
    Pages 211-232
  9. Krishan L. Duggal, Aurel Bejancu
    Pages 233-252
  10. Krishan L. Duggal, Aurel Bejancu
    Pages 253-273
  11. Back Matter
    Pages 274-303

About this book

Introduction

This book is about the light like (degenerate) geometry of submanifolds needed to fill a gap in the general theory of submanifolds. The growing importance of light like hypersurfaces in mathematical physics, in particular their extensive use in relativity, and very limited information available on the general theory of lightlike submanifolds, motivated the present authors, in 1990, to do collaborative research on the subject matter of this book. Based on a series of author's papers (Bejancu [3], Bejancu-Duggal [1,3], Dug­ gal [13], Duggal-Bejancu [1,2,3]) and several other researchers, this volume was conceived and developed during the Fall '91 and Fall '94 visits of Bejancu to the University of Windsor, Canada. The primary difference between the lightlike submanifold and that of its non­ degenerate counterpart arises due to the fact that in the first case, the normal vector bundle intersects with the tangent bundle of the submanifold. Thus, one fails to use, in the usual way, the theory of non-degenerate submanifolds (cf. Chen [1]) to define the induced geometric objects (such as linear connection, second fundamental form, Gauss and Weingarten equations) on the light like submanifold. Some work is known on null hypersurfaces and degenerate submanifolds (see an up-to-date list of references on pages 138 and 140 respectively). Our approach, in this book, has the following outstanding features: (a) It is the first-ever attempt of an up-to-date information on null curves, lightlike hypersur­ faces and submanifolds, consistent with the theory of non-degenerate submanifolds.

Keywords

differential geometry geometry manifold mathematical physics relativity theory of relativity

Authors and affiliations

  • Krishan L. Duggal
    • 1
  • Aurel Bejancu
    • 2
  1. 1.University of WindsorWindsorCanada
  2. 2.Polytechnic Institute of IaşiIaşiRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-2089-2
  • Copyright Information Springer Science+Business Media B.V. 1996
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4678-9
  • Online ISBN 978-94-017-2089-2
  • Buy this book on publisher's site