The type number on real hypersurfaces in a quaternion space form

Real Hypersurfaces of a Complex Space Form

In this paper, we show that an n-dimensional connected noncompact Ricci soliton isometrically immersed in the ‡at complex space form (C n+1 2 ; J; h; i), with potential vector …eld of the Ricci soliton is the characteristic vector …eld of the real hypersurface is an Einstein manifold. We classify connected Hopf hypersurfaces in the ‡at complex space form (C n+1 2 ; J; h; i) and also obtain a ch...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Hypersurfaces of a Sasakian space form with recurrent shape operator

Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.

Real Hypersurfaces in a Euclidean Complex Space Form

Let M be an orientable connected and compact real hypersurface of the complex space form C(n+1)/2. If the mean curvature α and the function f = g(Aξ, ξ) of hypersurface M satisfy the inequalityn2α2 ≤ (n2 − 1)δ + f 2, where ξ is the characteristic vector field,A is the shape operator and (n− 1)δ is the infimum of the Ricci curvatures of hypersurface M , then it is shown that α is a constant and ...

Pseudo Ricci symmetric real hypersurfaces of a complex projective space

Pseudo Ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo Ricci symmetric real hypersurfaces of the complex projective space CPn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.