2008/10/17 by S. L. Druta, Druta, S. L.
Mathematics · #53C07 #53C15 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C07 #msc:53C15 #msc:53C55
paper · pdf · doi:10.48550/arxiv.0810.3195
16 pages
arxiv created 2008/10/17 · arxiv updated 2009/12/01
We study the conditions under which the cotangent bundle T^*M of a Riemaannian manifold (M,g), endowed with a Kählerian structure (G,J) of general natural lift type (see \citeDruta1), is Einstein. We first obtain a general natural Kähler-Einstein structure on the cotangent bundle T^*M. In this case, a certain parameter, λ involved in the condition for (T^*M,G,J) to be a Kählerian manifold, is expressed as a rational function of the other two, the value of the constant sectional curvature, c, of the base manifold (M,g) and the constant ρ involved in the condition for the structure of being Einstein. This expression of λ is just that involved in the condition for the Kählerian manifold to have constant holomorphic sectional curvature (see \citeDruta2). In the second case, we obtain a general natural Kähler-Einstein structure only on T0M, the bundle of nonzero cotangent vectors to M. For this structure, λ is expressed as another function of the other two parameters, their derivatives, c and ρ.