Generalized cylinders in semi-Riemannian and spin geometry

By Christian Bär, P. Gauduchon, Andrei Moroianu. 2003

184 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/610df0ec56a778285be5604ebfc886b3b1441b80

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

Generalized Killing spinors in dimension 5 (2005, background): “We first give an example of a hypo structure such that A does not satisfy the Codazzi equation, proving that Theorem 4.4 is in some sense more general than the theorem of Bär, Gauduchon and Moroianu [4].”
Smooth Yamabe invariant and surgery (2008, methodology): “This is a generalized cylinder metric as studied in [11].”