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Zbl 1118.53042
Loubeau, Eric; Montaldo, Stefano; Oniciuc, Cezar
The biharmonic stress-energy tensor and the Gauss map. (English)
[A] Mladenov, Iva\"ilo (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. 234-245 (2007). ISBN 978-954-8495-37-0/pbk

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 2000:: *53C43 Differential geometric aspects of harmonic maps
58E11 Critical metrics in infinite-dimensional spaces
53C80 Appl. of global differential geometry to physics
53C40 Submanifolds (differential geometry)

Keywords: stress-energy tensor; Willmore surfaces; pseudo-umbilicity

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