On conformally Kähler, Einstein manifolds

On Conformally Kähler, Einstein Manifolds

We prove that any compact complex surface with c1 > 0 admits an Einstein metric which is conformally related to a Kähler metric. The key new ingredient is the existence of such a metric on the blow-up CP2#2CP2 of the complex projective plane at two distinct points.

Locally conformally Kähler manifolds with potential

A locally conformally Kähler (LCK) manifold M is one which is covered by a Kähler manifold M̃ with the deck transform group acting conformally on M̃ . If M admits a holomorphic flow, acting on M̃ conformally, it is called a Vaisman manifold. Neither the class of LCK manifolds nor that of Vaisman manifolds is stable under small deformations. We define a new class of LCK-manifolds, called LCK manifo...

Ricci Flow on Kähler-einstein Manifolds

Twistors in Conformally Flat Einstein Four-manifolds

Abstract. This paper studies the two-component spinor form of massive spin2 potentials in conformally flat Einstein four-manifolds. Following earlier work in the literature, a nonvanishing cosmological constant makes it necessary to introduce a supercovariant derivative operator. The analysis of supergauge transformations of primary and secondary potentials for spin 3 2 shows that the gauge fre...

Construction of conformally compact Einstein manifolds

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products of Kähler-Einstein manifolds. We compute the associated conformal invariants, i.e., the renormalized volume in even dimensions and the conformal anomaly in ...