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

Abstract

We study the conditions under which a Kählerian structure $(G,J)$ of general natural lift type on the cotangent bundle $T^{\ast }M$ of a Riemannian manifold $(M,g)$ has constant holomorphic sectional curvature. We obtain that a certain parameter involved in the condition for $(T^{\ast }M,G,J)$ to be a Kählerian 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 Kählerian structure $(G,J)$.

14 pages

References in corpus (1)

• A locally symmetric Kaehler Einstein structure on a tube in the nonzero cotangent bundle of a space form