Closed free hyperelastic curves in the hyperbolic plane and Chen-Willmore rotational hypersurfaces |
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| Authors: | J Arroyo O J Garay M Barros |
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| Institution: | (1) Departamento de Matemáticas, Universidad del pais Vasco/Euskal Herriko Unibertsitatea, Aptdo. 644, 48080 Bilbao, Spain;(2) Departmento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain |
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| Abstract: | We show that closed Chen-Willmore rotational hypersurfaces of nonnegative curved real space forms are shaped on closed hyperelastic
curves of the hyperbolic plane. Then, we study the variational problem associated to this class of curves, proving that there
exist a rationally dependent family of closed solutions. They give rise to the first non-trivial examples of Chen-Willmore
hypersurfaces in real space forms.
Research partially supported by a MCYT-FEDER grant No. BFM2001-2871-C04 and by a UPV grant 9/UPV00127.310-13574/01. |
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