A basic inequality for submanifolds in a cosymplectic space form.
In a nonflat complex space form (namely, a complex projective space or a complex hyperbolic space), real hypersurfaces admit an almost contact metric structure induced from the ambient space. As a matter of course, many geometers have investigated real hypersurfaces in a nonflat complex space form from the viewpoint of almost contact metric geometry. On the other hand, it is known that the tensor field
In the class of real hypersurfaces isometrically immersed into a nonflat complex space form of constant holomorphic sectional curvature which is either a complex projective space or...
We give a characterization of totally -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form in terms of totally umbilical condition for the holomorphic distribution on real hypersurfaces. We prove that if the shape operator of a real hypersurface of a complex space form , , , satisfies for any , being a function, where is the holomorphic distribution on , then is a totally -umbilical real hypersurface or locally congruent to a ruled real hypersurface....
A classification theorem is obtained for submanifolds with parallel second fundamental form of an 𝑆-manifold whose invariant f-sectional curvature is constant.