Symmetries and Kähler-Einstein metrics

Claudio Arezzo; Alessandro Ghigi

Displaying similar documents to “Symmetries and Kähler-Einstein metrics”

Sasakian geometry, hypersurface singularities, and Einstein metrics

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Homogeneous Einstein metrics on flag manifolds.

Sakane, Y. (1999)

Lobachevskii Journal of Mathematics

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Kähler-Einstein metrics singular along a smooth divisor

Raffe Mazzeo (1999)

Journées équations aux dérivées partielles

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In this note we discuss some recent and ongoing joint work with Thalia Jeffres concerning the existence of Kähler-Einstein metrics on compact Kähler manifolds which have a prescribed incomplete singularity along a smooth divisor $D$ . We shall begin with a general discussion of the problem, and give a rough outline of the “classical” proof of existence in the smooth case, due to Yau and Aubin, where no singularities are prescribed. Following this is a discussion of the geometry of the conical...

Self-dual Kähler manifolds and Einstein manifolds of dimension four

Andrzej Derdziński (1983)

Compositio Mathematica

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Einstein metrics and smooth structures.

Kotschick, D. (1998)

Geometry & Topology

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Homogeneous Einstein metrics on Stiefel manifolds

Andreas Arvanitoyeorgos (1996)

Commentationes Mathematicae Universitatis Carolinae

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A Stiefel manifold $V_{k} 𝐑^{n}$ is the set of orthonormal $k$ -frames in $𝐑^{n}$ , and it is diffeomorphic to the homogeneous space $S O (n) / S O (n - k)$ . We study $S O (n)$ -invariant Einstein metrics on this space. We determine when the standard metric on $S O (n) / S O (n - k)$ is Einstein, and we give an explicit solution to the Einstein equation for the space $V_{2} 𝐑^{n}$ .