The Ricci tensor of an almost homogenous Kaehler manifold

Details The Ricci tensor of an almost homogenous Kaehler manifold The Ricci tensor of an almost homogenous Kaehler manifold

2001-01-21

arxiv.org/abs/math/0101172v1

Mathematics

Differential Geometry

Scientific paper

We determine an explicit expression for the Ricci tensor of a K-manifold, that is of a compact Kaehler manifold M with vanishing first Betti number, on which a semisimple group G of biholomorphic isometries acts with an orbit of codimension one. We also prove that the Kaehler form and the Ricci form of M are uniquely determined by two special curves with values in g = Lie(G), say Z, Z': R \to g = Lie(G) and we show how the curve Z' is determined by the curve Z. These results are used in another work with F. Podesta', where new examples of non-homogeneous compact Kaehler-Einstein manifolds with positive first Chern class are constructed.

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