Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAn Obata-type characterization of doubly-warped product Kahler manifolds
116
0
0.0
(
0
)
Authors
Nicolas Ginoux
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 doubly warped product manifolds. We also prove the necessary and sufficient condition for a doubly warped product manifold to be a warped product manifold. We obtain some results for Einstein doubly warped product manifold and Einstein-like doubly warped product manifold of class A with respect to a semi-symmetric metric connection.
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 a characterization. To this end we obtain an inequality for the squared norm of second fundamental form in terms of the warping function and the slant angle. The equality case is also discussed.
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 the results of Hessian equations and Hessian quotient equations.
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 which can be written as a twisted product are those of constant curvature.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
