General Notion of Curvature in Catastrophe Theory Terms
Abstract
We introduce a new notion of a curvature of a superconnection, different from the one obtained by a purely algebraic analogy with the curvature of a linear connection. The naturalness of this new notion of a curvature of a superconnection comes from the study of singularities of smooth sections of vector bundles (Catastrophe Theory). We demonstrate that the classical examples of obstructions to a local equivalence: exterior differential for 2-forms, Riemannian tensor, Weil tensor, curvature of a linear connection and Nijenhuis tensor can be treated in terms of one general approach. This approach, applied to the superconnection leads to a new notion of a curvature (proposed in this paper) of a superconnection.
Keywords
Cite
@article{arxiv.0802.2187,
title = {General Notion of Curvature in Catastrophe Theory Terms},
author = {Petko Nikolov and Lora Nikolova and Gergana Ruseva},
journal= {arXiv preprint arXiv:0802.2187},
year = {2008}
}
Comments
13 pages, Ninth International Conference on Geometry, Integrability and Quantization, 2007