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Einstein metrics in projective geometry
projective differential geometry Einstein metrics conformal differential geometry
2012/7/11
It is well known that pseudo-Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined...
On the classification of homogeneous Einstein metrics on generalized flag manifolds with $b_2(M)=1$
Homogeneous Einstein metric flag manifold second Betti number finiteness conjecture twistor fibration
2012/6/25
We study homogeneous Einstein metrics for a class of compact homogeneous spaces, namely generalized flag manifolds $G/H$ with second Betti number $b_{2}(G/H)=1$. There are 33 such manifolds which have...
Einstein metrics and Yamabe invariants of weighted projective spaces
Einstein metrics Yamabe invariants weighted projective spaces Differential Geometry
2012/6/25
An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe in...