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| A Characterization of the Standard Tori in C2 as Compact Lagrangian ξ-Submanifolds* |
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Citation： |
Xingxiao LI.A Characterization of the Standard Tori in C2 as Compact Lagrangian ξ-Submanifolds*[J].Chinese Annals of Mathematics B,2022,43(3):473~482 |
| Page view： 519
Net amount： 437 |
Authors： |
Xingxiao LI; |
Foundation： |
National Natural Science Foundation of China (Nos. 11671121,11871197). |
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| Abstract： |
In this paper, the authors give a characterization theorem for the standard tori S1(a) × S1(b), a, b > 0, as the compact Lagrangian ξ-submanifolds in the two-dimensional complex Euclidean space C2 , and obtain the best version of a former rigidity theorem for compact Lagrangian ξ-submanifold in C2 . Furthermore, their argument in this paper also proves a new rigidity theorem which is a direct generalization of a rigidity theorem by Li and Wang for Lagrangian self-shrinkers in C2. |
Keywords： |
ξ-Submanifold, the Second fundamental form, Mean curvature vector,Standard tori |
Classification： |
53A30, 53B25 |
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