Abstract
In this paper, the authors give a characterization theorem for the standard tori \(\mathbb{S}^1(a) \times \mathbb{S}^1(b)\), 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.
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The authors would like to thank the reviewer’s careful revisions and suggestions, which are helpful for improving our manuscript.
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This work was supported by the National Natural Science Foundation of China (Nos. 11671121, 11871197).
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Li, X., Xu, R. A Characterization of the Standard Tori in ℂ2 as Compact Lagrangian ξ-Submanifolds. Chin. Ann. Math. Ser. B 43, 473–484 (2022). https://doi.org/10.1007/s11401-022-0336-3
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DOI: https://doi.org/10.1007/s11401-022-0336-3