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
kinematic Euclidean By using the moving frame method, the authors obtain a kind of asymmetric formulas for the total mean curvatures of hypersurfaces in the n-dimensional space
The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains a...The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11001016)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No. 20100003120003)the Program for Changjiang Scholars and Innovative Research Team in University
文摘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.
基金supported by the National Natural Science Foundation of China(No.11271302)Chongqing Natural Science Foundation(No.cstc2011jj A00026)
文摘kinematic Euclidean By using the moving frame method, the authors obtain a kind of asymmetric formulas for the total mean curvatures of hypersurfaces in the n-dimensional space
基金Project supported by the Spanish Ministry of Science and Technology Grants MTM2005-O8689-G02-02 and MTM 2004-06015-C02-01.
文摘The authors derive a formula for the volume of a compact domain in a symmetric space from normal sections through a special submanifold in the symmetric space.This formula generalizes the volume of classical domains as tubes or domains given as motions along the submanifold.Finally,some stereological considerations regarding this formula are provided.
