Curvature and pseudoconvexity on complex manifolds

✍ Scribed by B Wong

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 356 KB
• Volume: 37
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1016/0001-8708(80)90029-8

✦ Synopsis

The purpose of this note is to discuss several problems in hyperbolic complex analysis, primarily on the relationship between curvature and convexity conditions on certain Kahler manifolds.

DEFINITION.

Let p be a point in a Riemannian manifold (M, g), a nontrivial Jacobi vector field J(t) vanishing at P along a geodesic c(t) with c(0) = P satisfies Jacobi-growth condition iff d/dt(J(t), J(t)) > 0 for all t.

DEFINITION.

Let (M, g) be a complete Riemannian manifold a convex center P E M is a point such that any non-trivial Jacobi vector field vanishing at P along any geodesic passing through P must satisfy the Jacobi-growth condition.