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. For the entire collection see [Zbl 1108.53003
|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)|