Calculations of Lie derivatives reveal characterizations of homogeneous real hypersurfaces in complex spaces, suggesting new insights.
In this paper we calculate the Lie derivatives of homogeneous structure tensors of homogeneous real hypersurfaces in nonflat complex space forms in the direction of the structure vector field. Using these results, we give two characterization theorems of a homogeneous real hypersurface of type (A) in a nonflat complex space form.
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Fujiki et al. (2019) studied this question.
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