Asymptotic expansions of complete Kähler-Einstein metrics with finite volume on quasi-projective manifolds

Higher canonical asymptotics of Kähler–Einstein metrics on quasi-projective manifolds

We derive a canonical asymptotic expansion up to infinite order of the Kähler–Einstein metric on a quasi-projective manifold, which can be compactified by adding a divisor with simple normal crossings. Characterized by the log filtration of the Cheng–Yau Hölder ring, the asymptotics are obtained by constructing an initial Kähler metric, deriving certain iteration formula and applying the isomor...

Quasi-potentials and Kähler–Einstein metrics on flag manifolds, II

For a homogeneous space G/P , where P is a parabolic subgroup of a complex semisimple group G, an explicit Kähler–Einstein metric on it is constructed. The Einstein constant for the metric is 1. Therefore, the intersection number of the first Chern class of the holomorphic tangent bundle of G/P coincides with the volume of G/P with respect to this Kähler–Einstein metric, thus enabling us to com...

Warped product and quasi-Einstein metrics

Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...

Ricci Flow on Kähler-einstein Manifolds

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.