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VOL. 9 | 2008 The General Notion of a Curvature in Catastrophe Theory Terms
Petko Nikolov, Lora Nikolova, Gergana Ruseva

Editor(s) Ivaïlo M. Mladenov


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.


Published: 1 January 2008
First available in Project Euclid: 13 July 2015

zbMATH: 1192.53027
MathSciNet: MR2436278

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

Rights: Copyright © 2008 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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