S.H. Kon

Warped Product Semi-Invariant Submanifolds of Nearly Cosymplectic Manifolds

We study warped product semi-invariant submanifolds of nearly cosymplectic manifolds. We prove that the warped product of the type 𝑀⟂×𝑓𝑀𝑇 is a usual Riemannian product of 𝑀⟂ and 𝑀𝑇, where 𝑀⟂ and 𝑀𝑇 are anti-invariant and invariant submanifolds of a nearly cosymplectic manifold 𝑀, respectively. Thus we consider the warped product of the type 𝑀𝑇×𝑓𝑀⟂ and obtain a characterization for such type of warped product.

On characterizations of real hypersurfaces in a complex space form with eta-parallel shape operator.

In this paper, we study real hypersurfaces in a non-flat complex space form with n-parallel shape operator. Several partial characterizations of these real of these real hypersurfaces are obtained.

Real hypersurfaces in a complex space form with a condition on the structure Jacobi operator

In this paper we classify the real hypersurfaces in a non-flat complex space form with its structure Jacobi operator Rξ satisfying (∇XRξ)ξ = 0, for all vector fields X in the maximal holomorphic distribution D. With this result, we prove the non-existence of real hypersurfaces with D-parallel as well as D-recurrent structure Jacobi operator in complex projective and hyperbolic spaces. We can also prove the non-existence of real hypersurfaces with recurrent structure Jacobi operator in a non-flat complex space form as a corollary.

On the zeros of Hilbert spaces of analytic functions

An attempt is made to characterise the zeros of some Hilbert spaces of analytic functions means of their kernel functions. Results on the zeros of functions in D Φ and their uniqueness s are included, in particular we give an affirmative answer to a question of Shapiro and Shield