Abstract
In the theory of several complex variables pseudoconvexity is well known and in hermitian geometry holomorphic bisectional curvature is introduced by Goldberg and Kobayashi ([3]). In this paper we shall show three theorems concerning pseudoconvexity and holomorphic bisectional curvature. At first we shall be concerned with the complement of compact analytic sets and q-convex domains on k~hler manifolds and prove Theorems I,II (@ 3). Secondly we shall consider the local behavior of an energy function and give a differential geometric interpretation of holomorphic bisectional curvature (Theorem III in §4). In order to prove the theorems, we shall prepare a lemma, which gives us an explicit formula of laplacians of lengths and energies for a special family of curves (~ 2).
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