Proceedings of the International Conference on Geometry, Integrability and Quantization

The Biharmonic Stress-Energy Tensor and the Gauss Map

Eric Loubeau, Stefano Montaldo, and Cezar Oniciuc

Abstract

We consider the energy and bienergy functionals as variational problems on the set of Riemannian metrics and present a study of the bi- harmonic stress-energy tensor. This approach is then applied to characterize weak conformality of the Gauss map of a submanifold. Finally, working at the level of functionals, we recover a result of Weiner linking Willmore surfaces and pseudo-umbilicity.

Article information

Source
Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Manuel de León, eds. (Sofia: Softex, 2007), 234-245

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436792832

Digital Object Identifier
doi:10.7546/giq-8-2007-234-245

Mathematical Reviews number (MathSciNet)
MR2341207

Zentralblatt MATH identifier
1118.53042

Citation

Loubeau, Eric; Montaldo, Stefano; Oniciuc, Cezar. The Biharmonic Stress-Energy Tensor and the Gauss Map. Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, 234--245, Softex, Sofia, Bulgaria, 2007. doi:10.7546/giq-8-2007-234-245. https://projecteuclid.org/euclid.pgiq/1436792832


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