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We give a characterization {sl `a la Obata} for certain families of Kahler manifolds. These results are in the same line as other extensions of the well-known Obatas rigidity theorem from cite{Obata62}, like for instance the generalizations in cite{RanjSant97} and cite{Santhanam07}. Moreover, we give a complete description of the so-called Kahler doubly-warped product structures whose underlying metric is Einstein.
In this paper, we study the doubly warped product manifolds with semisymmetric metric connection. We derive the curvatures formulas for doubly warped product manifold with semi-symmetric metric connection in terms of curvatures of components of doubl
Non-existence of warped product semi-slant submanifolds of Kaehler manifolds was proved in [17], it is interesting to find their existence. In this paper, we prove the existence of warped product semi-slant submanifolds of nearly Kaehler manifolds by
In this paper we consider Serrins overdetermined problems in warped product manifolds and we prove Serrins type rigidity results by using the P-function approach introduced by Weinberger.
In this paper, we consider Hessian equations with its structure as a combination of elementary symmetric functions on closed Kahler manifolds. We provide a sufficient and necessary condition for the solvability of these equations, which generalize th
We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds whi