Abstract
In this note we consider Lagrangian Bonnet problem for Lagrangian surfaces in complex space forms. We first give a Bonnet type theorem for conformal Lagrangian surfaces in complex space forms, then we show that any compact Lagrangian surface in the complex space form admits at most one other global isometric Lagrangian surface with the same mean curvature form, unless the Maslov form is conformal. These two Lagrangian surfaces are then called Lagrangian Bonnet pairs. We also studied Lagrangian Bonnet surfaces in complex space forms, and obtain some characterizations of such surfaces.
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The authors would like to thank Professor Zizhou Tang for his constant encouragement.
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The second author was supported by NSFC (Grant Nos. 11671223 and 11831005); The third author would like to thank the Hong Kong University of Science & Technology for the support during the project
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He, H.X., Ma, H. & Wang, E.X. Lagrangian Bonnet Problems in Complex Space Forms. Acta. Math. Sin.-English Ser. 35, 1357–1366 (2019). https://doi.org/10.1007/s10114-019-8102-5
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DOI: https://doi.org/10.1007/s10114-019-8102-5