Mathematische Zeitschrift

, Volume 249, Issue 3, pp 545–580

Generalized cylinders in semi-Riemannian and spin geometry

Authors

    • Institut für MathematikUniversität Potsdam
  • Paul Gauduchon
    • Centre de MathématiquesÉcole Polytechnique
  • Andrei Moroianu
    • Centre de MathématiquesÉcole Polytechnique
Article

DOI: 10.1007/s00209-004-0718-0

Cite this article as:
Bär, C., Gauduchon, P. & Moroianu, A. Math. Z. (2005) 249: 545. doi:10.1007/s00209-004-0718-0

Abstract.

We use a construction which we call generalized cylinders to give a new proof of the fundamental theorem of hypersurface theory. It has the advantage of being very simple and the result directly extends to semi-Riemannian manifolds and to embeddings into spaces of constant curvature. We also give a new way to identify spinors for different metrics and to derive the variation formula for the Dirac operator. Moreover, we show that generalized Killing spinors for Codazzi tensors are restrictions of parallel spinors. Finally, we study the space of Lorentzian metrics and give a criterion when two Lorentzian metrics on a manifold can be joined in a natural manner by a 1-parameter family of such metrics.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005