Let M^n be a compact Willmore submanifold in the unit sphere Sn＋p. In this note, we investigate the first eigenvalue of the SchrSdinger operator L = -△ - q on M, where q is some potential function on M, and present...Let M^n be a compact Willmore submanifold in the unit sphere Sn＋p. In this note, we investigate the first eigenvalue of the SchrSdinger operator L = -△ - q on M, where q is some potential function on M, and present a gap estimate for the first eigenvalue of L.展开更多
In this paper,we show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore,hence all focal submanifolds of isoparametric hypersurfaces in th...In this paper,we show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore,hence all focal submanifolds of isoparametric hypersurfaces in the sphere are Willmore.展开更多
The authors study the regular submanifolds in the conformal space Qp^n and introduce the submanifold theory in the conformal space Qp^n. The first variation formula of the Willmore volume functional of pseudo-Riema...The authors study the regular submanifolds in the conformal space Qp^n and introduce the submanifold theory in the conformal space Qp^n. The first variation formula of the Willmore volume functional of pseudo-Riemannian submanifolds in the conformal space Qp^n is given. Finally, the conformal isotropic submanifolds in the conformal space展开更多
基金Supported by the National Natural Science Foundation of China(11071211)the Zhejiang Natural Science Foundation of China
文摘Let M^n be a compact Willmore submanifold in the unit sphere Sn＋p. In this note, we investigate the first eigenvalue of the SchrSdinger operator L = -△ - q on M, where q is some potential function on M, and present a gap estimate for the first eigenvalue of L.
基金Supported by National Natural Science Foundation of China(Grant Nos.11401151,11326071)
文摘In this paper,we show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore,hence all focal submanifolds of isoparametric hypersurfaces in the sphere are Willmore.
基金Project supported by the National Natural Science Foundation of China(No.10971055)the Natural Science Foundation of the Educational Commission of Hubei province(Key Program)(No.D1120111007)
文摘The authors study the regular submanifolds in the conformal space Qp^n and introduce the submanifold theory in the conformal space Qp^n. The first variation formula of the Willmore volume functional of pseudo-Riemannian submanifolds in the conformal space Qp^n is given. Finally, the conformal isotropic submanifolds in the conformal space
