The biharmonic stress-energy tensor and the Gauss map

Details The biharmonic stress-energy tensor and the Gauss map The biharmonic stress-energy tensor and the Gauss map

2006-09-23

arxiv.org/abs/math/0609661v1

Mathematics

Differential Geometry

Contribution to the Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, Varna 2006

Scientific paper

We consider the energy and bienergy functionals as variational problems on the set of Riemannian metrics and present a study of the biharmonic stress-energy tensor. This approach is then applied to characterise 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.

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