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.

We determine when the Hopf vector fields on orientable real hypersurfaces (M, g) in complex space forms are minimal or harmonic. Furthermore, we determine when these vector fields give rise to harmonic maps from (M, g) to the unit tangent sphere bundle (T1M, gS). In particular, we consider the special case of Hopf hypersurfaces and of ruled hypersurfaces. The Hopf vector fields on Hopf hypersur...

Hypersurfaces in complex projective spaces defined by homogeneous polynomials are important topological objects, arising naturally in algebra, geometry and topology. It was first noted by Thom, the diffeomorphism type of smooth hypersurfaces depends only on the degree of the defining polynomial; i.e., two n-dimensional smooth hypersurfaces in CPn+1 are diffeomorphic if and only if they have equ...

We study various classes of real hypersurfaces that are not embeddable into more special hypersurfaces in higher dimension, such as spheres, real algebraic compact strongly pseudoconvex hypersurfaces or compact pseudoconvex hypersurfaces of finite type. We conclude by stating some open problems.

We classify four-dimensional quasismooth weighted hypersurfaces with small canonical class, and verify a conjecture of Johnson and Kollár on infinite series of quasismooth hypersurfaces with anticanonical hyperplane section in the case of fourfolds. By considering the quotient singularities that arise, we classify those weighted hypersurfaces that are canonical, Calabi–Yau, and Fano fourfolds. ...

We study lightlike hypersurfaces of a semi-Riemannian product manifold. We introduce a class of lightlike hypersurfaces called screen semi-invariant lightlike hypersurfaces and radical antiinvariant lightlike hypersurfaces. We consider lightlike hypersurfaces with respect to a quartersymmetric nonmetric connection which is determined by the product structure. We give some equivalent conditions ...