The biharmonic stress-energy tensor and the Gauss map
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.
Contribution to the Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, Varna 2006