Related papers: A locally symmetric Kaehler Einstein structure on …

Given an Einstein structure with positive scalar curvature on a four-dimensional Riemannian manifolds, that is $Ric=\lambda g$ for some positive constant $\lambda$. For convenience, the Ricci curvature is always normalized to $Ric=1$. A…

We construct Einstein metrics of non-positive scalar curvature on certain solid torus bundles over a Fano Kahler-Einstein manifold. We show, among other things, that the negative Einstein metrics are conformally compact, and the Ricci-flat…

We show that the unit tangent bundle of S^4 and a real cohomology CP^3 admit Riemannian metrics with positive sectional curvature almost everywhere. These are the only examples so far with positive curvature almost everywhere that are not…

We provide a classification of Einstein submanifolds in space forms with flat normal bundle and parallel mean curvature. This extends a previous result due to Dajczer and Tojeiro for isometric immersions of Riemannian manifolds with…

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the…

In this paper, we show that every harmonic map from a compact K\"ahler manifold with uniformly RC-positive curvature to a Riemannian manifold with non-positive complex sectional curvature is constant. In particular, there is no non-constant…

We study the geometric properties of the base manifold for the unit tangent bundle satisfying the $\eta$-Einstein condition with the standard contact metric structure. One of the main theorems is that the unit tangent bundle of…

In this paper, we investigate the geometry of Einstein-type equation on a Riemannian manifold, unifying various particular geometric structures recently studied in the literature, such as critical point equation and vacuum static equation.…

We will discuss in this paper homogeneous locally conformally Keahler (or shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds from various aspects of study in the field of l.c.K. geometry. We will provide a survey…

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on…

We investigate the Einstein equation with a positive cosmological constant for $4n+4$-dimensional metrics on bundles over Quaternionic K\"ahler base manifolds whose fibers are 4-dimensional Bianchi IX manifolds. The Einstein equations are…

In this paper we study a Riemanian metric on the tangent bundle $T(M)$ of a Riemannian manifold $M$ which generalizes the Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to $T(M)$ a…

The main result is that the qc-scalar curvature of a seven dimensional quaternionic contact Einstein manifold is a constant. In addition, we characterize qc-Einstein structures with certain flat vertical connection and develop their local…

We provide several results on the existence of metrics of non-negative sectional curvature on vector bundles over certain cohomogeneity one manifolds and homogeneous spaces up to suitable stabilization. Beside explicit constructions of the…

A Riemannian or pseudo-Riemannian (or conformal) structure is conformally Einstein if and only if there is a suitably generic parallel section of a certain vector bundle -- the so-called standard conformal tractor bundle. We show that this…

We consider closed manifolds that admit a metric locally isometric to a product of symmetric planes. For such manifolds, we prove that the Euler characteristic is an obstruction to the existence of flat structures, confirming an old…

For moduli space of stable parabolic bundles on a compact Riemann surface, we derive an explicit formula for the curvature of its canonical line bundle with respect to Quillen's metric and interpret it as a local index theorem for the…

Let $M$ be a Kaehler manifold, and consider the total space $T^*M$ of the cotangent bundle to $M$. We show that in the formal neighborhood of the zero section $M \subset T^*M$ the space $T^*M$ admits a canonical hyperkaehler structure,…

We give an elementary treatment of the existence of complete Kahler-Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n+1)-sphere.

In this paper the classification of left-invariant Riemannian metrics, up to the action of the automorphism group, on cotangent bundle of (2n+1)-dimensional Heisenberg group is presented. Also, it is proved that the complex structure on…