We prove that a complex compact manifold endowed with a Kehler Ricci soliton cannot be isometrically embedded in a complex projective space CPn in such a way that the Gauss map is rational, unless the metric is Einstein. This applies to hypersurfaces of complex compact homogeneous spaces canonically embedded in CPn. We moreover obtain two curvature constraints for invariant Kaehler Ricci solitons on complex manifolds acted on by a compact Lie group with cohomogeneity one.
Remarks on Kaehler-Ricci solitons
BEDULLI, LUCIO;
2015-01-01
Abstract
We prove that a complex compact manifold endowed with a Kehler Ricci soliton cannot be isometrically embedded in a complex projective space CPn in such a way that the Gauss map is rational, unless the metric is Einstein. This applies to hypersurfaces of complex compact homogeneous spaces canonically embedded in CPn. We moreover obtain two curvature constraints for invariant Kaehler Ricci solitons on complex manifolds acted on by a compact Lie group with cohomogeneity one.File in questo prodotto:
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