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

WANG, PENG

Glasgow mathematical journal, Tome 54 (2012) no. 3, pp. 517-528

Résumé

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 .

Détail

DOI : 10.1017/S0017089512000122

Mots-clés : MSC(2000): 53A30, 53B30

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