In this paper, we obtain a formula for submanifolds in Sn+p by calculating the Laplacian of the Moebius second fundamental form. Using this formula, we obtain some pinching theorems about the minimal eigenvalue of the...In this paper, we obtain a formula for submanifolds in Sn+p by calculating the Laplacian of the Moebius second fundamental form. Using this formula, we obtain some pinching theorems about the minimal eigenvalue of the Blaschke tensor.展开更多
The most important Moebius invariants in the Moebius differential geometry of submanifolds in S^n＋p are the Moebius metric g, the Moebius second fundamental form B, the Moebius form φ and the Blaschke tensor A. In t...The most important Moebius invariants in the Moebius differential geometry of submanifolds in S^n＋p are the Moebius metric g, the Moebius second fundamental form B, the Moebius form φ and the Blaschke tensor A. In this paper, we obtain the upper bound of the Moebius scalar curvature of submanifolds with parallel Moebius form in S^n＋p.展开更多
文摘In this paper, we obtain a formula for submanifolds in Sn+p by calculating the Laplacian of the Moebius second fundamental form. Using this formula, we obtain some pinching theorems about the minimal eigenvalue of the Blaschke tensor.
基金Supported by the NSF of China(10671087)Supported by the NSF of Jiangxi Province(2008GZS0024)
文摘The most important Moebius invariants in the Moebius differential geometry of submanifolds in S^n＋p are the Moebius metric g, the Moebius second fundamental form B, the Moebius form φ and the Blaschke tensor A. In this paper, we obtain the upper bound of the Moebius scalar curvature of submanifolds with parallel Moebius form in S^n＋p.
