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Differential-Geometric Structures On Manifolds

  • Krishan L. Duggal
  • Aurel Bejancu
Part of the Mathematics and Its Applications book series (MAIA, volume 364)

Abstract

In the present chapter we provide most of the prerequisites for reading the rest of the book. In the first two sections we present a review of vector bundles and introduce the main differential operators: Lie derivative, exterior differential, linear connection, general connection. Distributions on manifolds (known as non-holonomic spaces in classical terminology) are then introduced and studied by using both methods of vector fields and of differential 1-forms. We give here the characterization for the existence of a transversal distribution to a foliation, which is found to be very useful in Chapters 4 and 5 for a general study of lightlike submanifolds. In the last two sections we deal with semi-Riemannian manifolds and lightlike manifolds. While the geometry of a semi-Riemannian manifold is fully developed by using the Levi-Civita connection we stress the role of the radical distribution in studying the geometry of a lightlike manifold. The main formulas and results are expressed by using both the invariant form and the index form.

Keywords

Vector Field Vector Bundle Tensor Field Linear Connection Local Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

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

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