Abstract
We prove some differentiable sphere theorems and topological sphere theorems for Lagrangian submanifolds in Kähler manifold and Legendrian submanifolds in Sasaki space form.
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The authors would like to thank the referee for his/her careful reading and useful comments.
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Communicated by J. Jost.
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The first author was supported by the National Natural Science Foundation of China (Grant No. 11401440). Part of the work was finished when the first author was a visiting scholar at MIT supported by China Scholarship Council (CSC) and the Youth Talent Training Program of Wuhan University. The author would like to express his gratitude to Professor Tobias Colding for his invitation and to MIT for their hospitality. The second author was supported by the National Natural Science Foundation of China (Grant Nos. 11801420, 11971358) and the Youth Talent Training Program of Wuhan University. The author thanks the Max Planck Institute for Mathematics in the Sciences for good working conditions when this work was carried out. They also thank Dr. Yong Luo for helpful discussions.
