余切丛上一般自然Kähler结构的全纯Sectional Curvature
The Holomorphic Sectional Curvature of General Natural KÄhler Structures on Cotangent Bundles
摘要：
研究了黎曼流形$(M,g)$的余切丛$T^*M$上的一般自然提升型Kähler结构$(G,J)$具有常全纯截面曲率的条件.我们得到了$(T^*M,G,J)$是Kähler流形的条件中的一个参数，可以表示为基流形$(M,g)$的常截面曲率和一般自然Kähler结构$(G,J)$的常全纯截面曲率的有理函数.
英文摘要：
We study the conditions under which a Kählerian 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 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 $(G,J)$.
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