The Ricci tensor of an almost homogenous Kaehler manifold

2001/01/21 by Andrea Spiro, Spiro, Andrea
Mathematics · #53C25 #53C55 #57S15 #Differential Geometry (math.DG) #FOS: Mathematics #Quantum Algebra (math.QA) #math.DG #math.QA #msc:53C25 #msc:53C55 #msc:57S15

paper · pdf · doi:10.48550/arxiv.math/0101172

arxiv created 2001/01/21 · arxiv updated 2009/11/30

Abstract

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 → 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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