The biharmonic stress-energy tensor and the Gauss map.

*(English)* Zbl 1118.53042
Mladenov, Ivaïlo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9–14, 2006. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-37-0/pbk). 234-245 (2007).

Summary: 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 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.

##### MSC:

53C43 | Differential geometric aspects of harmonic maps |

58E11 | Critical metrics in infinite-dimensional spaces |

53C80 | Applications of global differential geometry to physics |

53C40 | Global submanifolds (differential geometry) |