Open Access
2012 A Better Calculus of Moving Surfaces
Pavel Grinfeld
J. Geom. Symmetry Phys. 26: 61-69 (2012). DOI: 10.7546/jgsp-26-2012-61-69


We introduce $\dot{\nabla}$, a new invariant time derivative with respect to a moving surface that is a modification of the classical $\delta /\delta $ -derivative. The new operator offers significant advantages over its predecessor. In particular, it produces zero when applied to the surface metric tensors $S_{\alpha \beta }$ and $S^{\alpha \beta }$ and therefore permits free juggling of surface indices in the calculus of moving surfaces identities. As a result, the table of essential differential relationships is cut in half. To illustrate the utility of the operator, we present a calculus of moving surfaces proof of the Gauss-Bonnet theorem for smooth closed two dimensional hypersurfaces.


Download Citation

Pavel Grinfeld. "A Better Calculus of Moving Surfaces." J. Geom. Symmetry Phys. 26 61 - 69, 2012.


Published: 2012
First available in Project Euclid: 25 May 2017

zbMATH: 06131401
MathSciNet: MR2986252
Digital Object Identifier: 10.7546/jgsp-26-2012-61-69

Rights: Copyright © 2012 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

Back to Top