This paper classifies real hypersurfaces regarding the shape, structure Lie, and contact Lie operators, indicating their parallel nature.
On real hypersurafces of the Kähler surface and , there are three typical operators: the shape operator, the structure Lie operator, and the contact Lie operator. In this paper, we study real hypersurfaces in and related to these operators. As the main results, we classify real hypersurfaces of both and for which one of the preceding three operators is either parallel or ‐parallel.
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Hu et al. (2025) studied this question.