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We study the conditions under which a K\"ahlerian structure $(G,J)$ ofgeneral natural lift type on the cotangent bundle $T^*M$ of a Riemannianmanifold $(M,g)$ has constant holomorphic sectional curvature. We obtain that acertain parameter involved in the condition for $(T^*M,G,J)$ to be aK\"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 generalnatural K\"ahlerian structure $(G,J)$.

The Holomorphic Sectional Curvature of General Natural K\"Ahler Structures on Cotangent Bundles