The Holomorphic Sectional Curvature of General Natural KÄhler Structures on Cotangent Bundles

Details The Holomorphic Sectional Curvature of General Natural KÄhler Structures on Cotangent Bundles The Holomorphic Sectional Curvature of General Natural KÄhler Structures on Cotangent Bundles

2008-10-09

arxiv.org/abs/0810.1652v1

Mathematics

Differential Geometry

14 pages

Scientific paper

We study the conditions under which a K\"ahlerian structure $(G,J)$ of general natural lift type on the cotangent bundle $T^*M$ of a Riemannian manifold $(M,g)$ has constant holomorphic sectional curvature. We obtain that a certain parameter involved in the condition for $(T^*M,G,J)$ to be a K\"ahlerian manifold, is expressed as a rational function of the other two, their derivatives, the constant sectional curvature of the base manifold $(M,g)$, and the constant holomorphic sectional curvature of the general natural K\"ahlerian structure $(G,J)$.

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