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Variational formulas of higher order mean curvatures 被引量:2
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作者 XU Ling GE JianQuan 《Science China Mathematics》 SCIE 2012年第10期2147-2158,共12页
In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total 2p-th mean curvature functional .M2p of a submanifold Mn in a general Riemannian manifold gn^n+m for p = 0, 1,..... In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total 2p-th mean curvature functional .M2p of a submanifold Mn in a general Riemannian manifold gn^n+m for p = 0, 1,..., [n/2]. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional M2p, called relatively 2p-minimal submanifolds, for all p. At last, we discuss the relations between relatively 2p-minimal submanifoIds and austere submanifolds in real space forms, as well as a special variational problem. 展开更多
关键词 2p-minimal mean curvature austere submanifold
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