摘要
Recently, Prof. Wu Guanglei and Chen Weihuan obtained the first variational formula of the Killing invariant of a submanifold in the Euclidean space, which is a generalization of the classical formula for the first variation of the volume. In this note, we extend their formula to a submanifold in the Riemannian manifold, and study further the e-minimal submanifold. Especially, we study the e-minimal submanifold of a sphere with second fundamental form of constant length, and extend the result of S. S. Chern, M. Do. Carmo and S. Kobayashi’s.
