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ON THE WILLMORE FUNCTIONAL OF 2-TORI IN SOME PRODUCT RIEMANNIAN MANIFOLDS

Published online by Cambridge University Press:  30 March 2012

PENG WANG
PENG WANG*
Affiliation:
Department of Mathematics, Tongji University, Siping Road 1239, Shanghai, 200092, People's Republic of China. e-mail: netwangpeng@tongji.edu.cn, netwangpeng@hotmail.com
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Abstract

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We discuss the minimum of Willmore functional of torus in a Riemannian manifold N, especially for the case that N is a product manifold. We show that when N = S2 × S1, the minimum of W(T2) is 0, and when N = R2 × S1, there exists no torus having least Willmore functional. When N = H2(−c) × S1, and x = γ × S1, the minimum of W(x) is .

Keywords

MSC(2000): 53A3053B30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 3 , September 2012 , pp. 517 - 528
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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