Details

Autor(en) / Beteiligte

• Leng, Yan
• Xu, Hong-Wei

Titel

The generalized Lu rigidity theorem for submanifolds with parallel mean curvature

Ist Teil von

• Manuscripta mathematica, 2018, Vol.155 (1-2), p.47-60

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2018

Quelle

Springer LINK 全文期刊数据库

Beschreibungen/Notizen

• Let M be an n -dimensional oriented compact submanifold with parallel mean curvature in the unit sphere S n + p . Denote by H and S the mean curvature and the squared length of the second fundamental form of M , respectively. We obtain a classification theorem of M if it satisfies S + λ 2 ≤ α ( n , H ) , where λ 2 is the second largest eigenvalue of the fundamental matrix and α ( n , H ) is defined as in Theorem B.