General Notion of Curvature in Catastrophe Theory Terms

Details General Notion of Curvature in Catastrophe Theory Terms General Notion of Curvature in Catastrophe Theory Terms

2008-02-15

arxiv.org/abs/0802.2187v1

Physics

Mathematical Physics

13 pages, Ninth International Conference on Geometry, Integrability and Quantization, 2007

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

General Notion of Curvature in Catastrophe Theory Terms 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 General Notion of Curvature in Catastrophe Theory Terms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and General Notion of Curvature in Catastrophe Theory Terms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-38473