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
文摘设π∶Nn+r→Nn′是R iem ann浸没,f∶Mm+r→Nn+r和f′∶Mm′→Nn′都是等距浸入,并假定M遵从R iem ann浸没π,我们证明:1)若M是N的全脐子流形,则M′是N′的全脐子流形.2)若f(M)是N的迷向子流形,则f(′M′)是N′的迷向子流形.3)如果M包含在N的一个全测地子流形Nm+r+1中,则M′包含在N′的一个全测地子流形Nm′+1中.特别地,我们得到复射影空间和四元数射影空间中子流形的S im ons型P inch ing定理及全脐子流形的一个特征.
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
