Willmore submanifolds in the unit sphere

• Autores: Zhen Guo
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 55, Fasc. 3, 2004, págs. 279-288
• Idioma: inglés
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• Resumen

  • In this paper we generalize the self-adjoint differential operator (used by Cheng-Yau) on hypersurfaces of a constant curvature manifold to general submanifolds. The generalized operator is no longer self-adjoint. However we present its adjoint operator. By using this operator we get the pinching theorem on Willmore submanifolds which is analogous to the pinching theorem on minimal submanifold of a sphere given by Simon and Chern-Do Carmo-Kobayashi.

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