The geometry of hypersurfaces of quasi-Kählerian manifolds. (English. Russian original) Zbl 0866.53042

Kirichenko, V. F.; Stepanova, L. V.

Russ. Math. Surv. 50, No. 2, 440-441 (1995); translation from Usp. Mat. Nauk 50, No. 2, 213-214 (1995).

The paper is devoted to the geometry of hypersurfaces in quasi-Kählerian manifolds. Among six theorems presented in the paper, we find the ones: on inducing of a quasi-Sasakian structure to a hypersurface of a nearly-Kählerian manifold; on a locally holomorphically isometric classification of \(\eta\)-umbilical hypersurfaces in \(2n\)-dimensional complex space forms; and, in such a manifold, on a characterization of \(\eta\)-Einstein hypersurfaces among quasi-Sasakian ones.

Reviewer: W.Waliszewski (Łódź)

MSC:

53C40	Global submanifolds
53C55	Global differential geometry of Hermitian and Kählerian manifolds
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords:

almost-Kähler; almost contact; nearly-Kähler; hypersurfaces; quasi-Kählerian manifolds; \(\eta\)-Einstein; quasi-Sasakian