Abstract Let M^2 be an umbilic-free surface in the unit sphere S^3. Four basic invariants of M^2 under the Moebius transformation group of S^3 are Moebius metric g, Blaschke tensor A, Moebius second fundamental form B...Abstract Let M^2 be an umbilic-free surface in the unit sphere S^3. Four basic invariants of M^2 under the Moebius transformation group of S^3 are Moebius metric g, Blaschke tensor A, Moebius second fundamental form B and Moebius form φ. We call the Blaschke tensor is isotropic if there exists a smooth function λ such that A = λg. In this paper, We classify all surfaces with isotropic Blaschke tensor in S^3.展开更多
Let Mn be an n-dimensional submanifold without umbilical points in the （n ＋ 1）-dimen- sional unit sphere Sn＋l. Four basic invariants of Mn under the Moebius transformation group of Sn＋1 are a 1-form Ф called moe...Let Mn be an n-dimensional submanifold without umbilical points in the （n ＋ 1）-dimen- sional unit sphere Sn＋l. Four basic invariants of Mn under the Moebius transformation group of Sn＋1 are a 1-form Ф called moebius form, a symmetric （0, 2） tensor A called Blaschke tensor, a symmetric （0, 2） tensor B called Moebius second fundamental form and a positive definite （0, 2） tensor g called Moebius metric. A symmetric （0,2） tensor D = A ＋ μB called para-Blaschke tensor, where μ is constant, is also an Moebius invariant. We call the para-Blaschke tensor is isotropic if there exists a function ,λ such that D = λg. One of the basic questions in Moebius geometry is to classify the hypersurfaces with isotropic para-Blaschke tensor. When λ is not constant, all hypersurfaces with isotropic para-Blaschke tensor are explicitly expressed in this paper.展开更多
文摘Abstract Let M^2 be an umbilic-free surface in the unit sphere S^3. Four basic invariants of M^2 under the Moebius transformation group of S^3 are Moebius metric g, Blaschke tensor A, Moebius second fundamental form B and Moebius form φ. We call the Blaschke tensor is isotropic if there exists a smooth function λ such that A = λg. In this paper, We classify all surfaces with isotropic Blaschke tensor in S^3.
基金supported by National Natural Science Foundation of China(Grant No.10861013)Academic Talents of Chuxiong Normal University(Grant No.09YJRC10)
文摘Let Mn be an n-dimensional submanifold without umbilical points in the （n ＋ 1）-dimen- sional unit sphere Sn＋l. Four basic invariants of Mn under the Moebius transformation group of Sn＋1 are a 1-form Ф called moebius form, a symmetric （0, 2） tensor A called Blaschke tensor, a symmetric （0, 2） tensor B called Moebius second fundamental form and a positive definite （0, 2） tensor g called Moebius metric. A symmetric （0,2） tensor D = A ＋ μB called para-Blaschke tensor, where μ is constant, is also an Moebius invariant. We call the para-Blaschke tensor is isotropic if there exists a function ,λ such that D = λg. One of the basic questions in Moebius geometry is to classify the hypersurfaces with isotropic para-Blaschke tensor. When λ is not constant, all hypersurfaces with isotropic para-Blaschke tensor are explicitly expressed in this paper.
