Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications

1. Front Matter

   Pages i-viii

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2. Algebraic Preliminaries

   • Krishan L. Duggal, Aurel Bejancu

   Pages 1-17

3. Differential-Geometric Structures On Manifolds

   • Krishan L. Duggal, Aurel Bejancu

   Pages 18-51

4. Geometry of Null Curves in Lorentz Manifolds

   • Krishan L. Duggal, Aurel Bejancu

   Pages 52-76

5. Lightlike Hypersurfaces of Semi-Riemannian Manifolds

   • Krishan L. Duggal, Aurel Bejancu

   Pages 77-138

6. Lightlike Submanifolds Of Semi-Riemannian Manifolds

   • Krishan L. Duggal, Aurel Bejancu

   Pages 139-189

7. CR Lightlike Submanifolds of Indefinite Kaehler Manifolds

   • Krishan L. Duggal, Aurel Bejancu

   Pages 190-210

8. Lightlike Hypersurfaces of Lorentz Framed Manifolds

   • Krishan L. Duggal, Aurel Bejancu

   Pages 211-232

9. Lightlike Hypersurfaces And Electromagnetism

   • Krishan L. Duggal, Aurel Bejancu

   Pages 233-252

10. Lightlike Hypersurfaces and General Relativity

    • Krishan L. Duggal, Aurel Bejancu

    Pages 253-273

11. Back Matter

    Pages 274-303

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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.

• differential geometry
• geometry
• manifold
• mathematical physics
• relativity
• theory of relativity
• partial differential equations

• University of Windsor, Windsor, Canada

  Krishan L. Duggal

• Polytechnic Institute of Iaşi, Iaşi, Romania

  Aurel Bejancu

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