The Möbius characterizations of Willmore tori and Veronese submanifolds in the unit sphere

• Autores: Zhen Guo, Haizhong Li, Changping Wang
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 241, Nº 2, 2009, págs. 227-242
• Idioma: inglés
• DOI: 10.2140/pjm.2009.241.227
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• Resumen

  • Suppose M is a m-dimensional submanifold without umbilic points in the (m + p)-dimensional unit sphere Sm+p. Four basic invariants of Mm under the Möbius transformation group of Sm+p are a symmetric positive definite 2-form g called the Möbius metric, a section B of the normal bundle called the Möbius second fundamental form, a 1-form F called the Möbius form, and a symmetric (0,2) tensor A called the Blaschke tensor. In the Möbius geometry of submanifolds, the most important examples of Möbius minimal submanifolds (also called Willmore submanifolds) are Willmore tori and Veronese submanifolds. In this paper, several fundamental inequalities of the Möbius geometry of submanifolds are established and the Möbius characterizations of Willmore tori and Veronese submanifolds are presented by using Möbius invariants.