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Levi-parallel hypersurfaces in a complex space form. (English) Zbl 1131.53025
Let \(M\) be a Hopf hypersurface of a complex space form of constant holomorphic sectional curvature \(c\neq 0\), i.e., its structure vector is a principal curvature vector. In 1999 the author defined the generalized Tanaka-Webster connection for real hypersurfaces in Kählerian manifolds [Publ. Math. 54, No. 3–4, 473–487 (1999; Zbl 0929.53029)]. The main theorem of the present paper classifies all real Hopf hypersurfaces of a complex space form, \(c\neq 0\), whose Levi form is parallel with respect to the generalized Tanaka-Webster connection.

MSC:
53C40 Global submanifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53D15 Almost contact and almost symplectic manifolds
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