Generalized Cylinders in Semi-Riemannian and Spin Geometry
Baer, Christian ; Gauduchon, Paul ; Moroianu, Andrei
arXiv, 0303095 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-03-07
Classification:  Mathematics - Differential Geometry,  Mathematical Physics,  53C27, 53A07, 53B30 
@article{0303095,
     author = {Baer, Christian and Gauduchon, Paul and Moroianu, Andrei},
     title = {Generalized Cylinders in Semi-Riemannian and Spin Geometry},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0303095}
}

Baer, Christian; Gauduchon, Paul; Moroianu, Andrei. Generalized Cylinders in Semi-Riemannian and Spin Geometry. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0303095/