Correction and addition: ``Bubbling out of Einstein manifolds''

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...

Bubbling solutions for supercritical problems on manifolds

Article history: Received 15 May 2014 Available online 10 November 2014 MSC: 35B10 35B33 35J08 58J05

Einstein Manifolds and Contact Geometry

We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.

Nearly Einstein Manifolds

The object of this paper is to define and study a new type of non-flat Riemannian manifold called nearly Einstein manifold. The notion of this nearly Einstein manifold has been established by an example and an existence theorem. Some geometric properties are obtained. AMS Mathematics Subject Classification (2010): 53C25.

Four - Manifolds without Einstein