Abstract
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 Mobius transformation group of Sm+p are a symmetric positive definite 2-form g called the Mobius metric, a section B of the normal bundle called the Mobius second fundamental form, a 1-form F called the Mobius form, and a symmetric (0,2) tensor A called the Blaschke tensor. In the Mobius geometry of submanifolds, the most important examples of Mobius minimal submanifolds (also called Willmore submanifolds) are Willmore tori and Veronese submanifolds. In this paper, several fundamental inequalities of the Mobius geometry of submanifolds are established and the Mobius characterizations of Willmore tori and Veronese submanifolds are presented by using Mobius invariants.
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