The Ricci tensor of an almost homogenous Kaehler manifold
Abstract
We determine an explicit expression for the Ricci tensor of a Kmanifold, 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 nonhomogeneous compact KaehlerEinstein manifolds with positive first Chern class are constructed.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2001
 arXiv:
 arXiv:math/0101172
 Bibcode:
 2001math......1172S
 Keywords:

 Differential Geometry;
 Quantum Algebra;
 53C55;
 53C25;
 57S15