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The biharmonic stress-energy tensor and the Gauss map

E. Loubeau·S. Montaldo·C. Oniciuc
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Abstract

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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E. Loubeau, S. Montaldo, C. Oniciuc. 2006-09-23. The biharmonic stress-energy tensor and the Gauss map. https://arxiv.org/abs/math/0609661

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