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Journal article
A BETTER CALCULUS OF MOVING SURFACES
Journal of geometry and symmetry in physics, v 26(JUNE), pp 61-69
01 Jan 2012
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
We introduce <(0) over dot>, 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.
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Details
- Title
- A BETTER CALCULUS OF MOVING SURFACES
- Creators
- Pavel Grinfeld - Drexel University
- Publication Details
- Journal of geometry and symmetry in physics, v 26(JUNE), pp 61-69
- Publisher
- Inst Biophysics & Biomedical Engineering, Bulgarian Acad Sciences
- Number of pages
- 9
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000436561900004
- Scopus ID
- 2-s2.0-84871337117
- Other Identifier
- 991019312437104721
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- Web of Science research areas
- Physics, Mathematical