Generalized Cylinders in Semi-Riemannian and Spin Geometry

Details Generalized Cylinders in Semi-Riemannian and Spin Geometry Generalized Cylinders in Semi-Riemannian and Spin Geometry

2003-03-07

arxiv.org/abs/math/0303095v1

Mathematische Zeitschrift 249 (2005), 545-580

Mathematics

Differential Geometry

29 pages, 2 figures

Scientific paper

10.1007/s00209-004-0718-0

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.

Affiliated with

Also associated with

No associations

Rating

Generalized Cylinders in Semi-Riemannian and Spin Geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Cylinders in Semi-Riemannian and Spin Geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Cylinders in Semi-Riemannian and Spin Geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-440785