On Calabi’s inhomogeneous Einstein-Kaehler manifolds

Lecture on Kaehler manifolds

New Inhomogeneous Einstein Metrics on Sphere Bundles Over Einstein-Kähler Manifolds

We construct new complete, compact, inhomogeneous Einstein metrics on S sphere bundles over 2n-dimensional Einstein-Kähler spaces K2n, for all n ≥ 1 and all m ≥ 1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of S with S bundles over K2n, for m > 1. Additionally, we construct new complete, noncompact Ricci-flat metrics with topologies S times R bundles ove...

On quasi Einstein manifolds

The object of the present paper is to study some properties of a quasi Einstein manifold. A non-trivial concrete example of a quasi Einstein manifold is also given.

Ricci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds

We obtain the expression of Ricci tensor for a $GCR$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $GCR$-lightlike submanifold of anindefinite complex space form. Moreover, we have proved that everyproper totally umbilical $GCR$-lightlike submanifold of anindefinite Kaehler manifold is a totally geodesic $GCR$-lightlikesubmanifold.

Conformal mappings preserving the Einstein tensor of Weyl manifolds

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...