Proceedings of the International Conference on Geometry, Integrability and Quantization

The General Notion of a Curvature in Catastrophe Theory Terms

Petko Nikolov, Lora Nikolova, and Gergana Ruseva

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 the singularities of smooth sections of vector bundles (Catastrophe Theory). We demonstrate that the classical examples of obstructions to a local equivalence: exterior differential for two-forms, Riemannian tensor, Weil tensor, curvature of a linear connection and Nijenhuis tensor can be treated in terms of some general approach. This approach, applied to the superconnection leads to a new notion of a curvature (proposed in the paper) of a superconnection.

Article information

Source
Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, ed. (Sofia: Softex, 2008), 265-179

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436793153

Digital Object Identifier
doi:10.7546/giq-9-2008-265-279

Mathematical Reviews number (MathSciNet)
MR2436278

Zentralblatt MATH identifier
1192.53027

Citation

Nikolov, Petko; Nikolova, Lora; Ruseva, Gergana. The General Notion of a Curvature in Catastrophe Theory Terms. Proceedings of the Ninth International Conference on Geometry, Integrability and Quantization, 265--179, Softex, Sofia, Bulgaria, 2008. doi:10.7546/giq-9-2008-265-279. https://projecteuclid.org/euclid.pgiq/1436793153


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