Abstract
In this paper the notion of k-th generalized Tanaka–Webster Einstein real hypersurfaces in non-flat complex space forms is introduced. Furthermore, three dimensional real hypersurfaces in non-flat complex space forms, which are k-th generalized Tanaka–Webster Einstein, are classified. Moreover, the notion of Ricci soliton for the k-th generalized Tanaka–Webster connection of a real hypersurface is also introduced and first results concerning the new notion and real hypersurfaces are provided. At the end of the paper, discussion and ideas of further research on the new notions is included.
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