We present an alternative proof of a nonexistence result for displaceable constant sectional curvature Lagrangian submanifolds under certain assumptions on the Lagrangian submanifold and on the ambient symplectically aspherical symplectic manifold. The proof utilizes an index relation relating the Maslov index, the Morse index and the Conley–Zehnder index for a periodic orbit of the flow of a specific Hamiltonian function, a result on this orbit’s Conley–Zehnder index and another result on the Morse indices for constant sectional curvature manifolds the utilization of which to prove nondisplaceability is new.

中文翻译：

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某些恒定截面曲率拉格朗日子流形的可移位性

我们提出了在拉格朗日子流形和环境对称非球面辛流形上的某些假设下，可位移的恒定截面曲率拉格朗日子流形不存在结果的替代证明。证明利用索引关系，将特定的哈密顿函数流的周期性轨道与Maslov索引，Morse索引和Conley-Zehnder索引相关联，该轨道的Conley-Zehnder索引的结果以及Morse索引的另一结果用于恒定截面曲率歧管在证明不可移位性方面的应用是新的。