The biharmonic stress-energy tensor and the Gauss map

2006/09/23 by E. Loubeau, Loubeau, E., Stefano Montaldo +3
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.math/0609661

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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