We consider real hypersurfaces M in complex projective space equipped with both the Levi-Civita and generalized Tanaka–Webster connections. Associated with the generalized Tanaka–Webster connection we can define a differential operator of first order. For any nonnull real number k and any symmetric tensor field of type (1,1) B on M, we can define a tensor field of type (1,2) on M, \(B^{(k)}_T\), related to Lie derivative and such a differential operator. We study symmetry and skew symmetry of the tensor \(A^{(k)}_T\) associated with the shape operator A of M.

中文翻译：

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复射影空间中实超曲面形状算子的李导数

我们考虑配备了 Levi-Civita 和广义 Tanaka-Webster 连接的复杂射影空间中的真实超曲面M。与广义的 Tanaka-Webster 连接相关联，我们可以定义一阶微分算子。对于任何非空实数ķ和类型（1,1）中的任对称张量场乙上中号，我们可以定义上式（1,2）的张量场中号，\（B ^ {（K）} _Ť\），与李导数和这样的微分算子有关。我们研究对称性和张量的斜对称\（A ^ {（K）} _Ť\）与形状运营商相关联甲的中号。