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This lecture concerns the metric Riemannian geometry of Einstein manifolds, which is a central theme in modern differential geometry and is deeply connected to a large variety of fundamental problems ...
The global additive and multiplicative properties of Laplace type operators acting on irreducible rank 1 symmetric spaces are considered. The explicit form of the zeta function on product spaces and o...
We study the renormalized volume of a conformally compact Einstein manifold. In even dimenions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the...
We study the renormalized volume of a conformally compact Einstein manifold. In even dimenions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the...
In this paper we introduce the notion of generalized quasi–Einstein manifold, which generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi–Einstein manifolds. We prove that a compl...
Seven-dimensional inhomogeneous Sasaki-Einstein manifolds $Y^{p,k}(KE_4)$ present a challenging example of AdS/CFT correspondence. At present, their field theory duals for $KE_4=\mathbb{CP}^2$ base ar...
In this paper we prove a number of triviality results for Einstein warped products and quasi-Einstein manifolds using different techniques and under assumptions of various nature. In particular we ob...
In joint work with Chen and Weber [7] , the author has elsewhere shown that CP2#2CP2 admits an Einstein metric. The present paper gives a new and rather different proof of this fact. Our results inclu...
In this study, we find the necessary conditions in order that a special class of generalized quasi-Einstein manifolds to be pseudo Riccisymmetric and R-harmonic. We also consider these type manifold...
In this study, we find the necessary conditions in order that a special class of generalized quasi-Einstein manifolds to be pseudo Riccisymmetric and R-harmonic. We also consider these type manifold...

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