A Generalized Bochner Technique and Its Application to the Study of Conformal Mappings

Abstract

This article is devoted to geometrical aspects of conformal mappings of complete Riemannian and Kählerian manifolds and uses the Bochner technique, one of the oldest and most important techniques in modern differential geometry. A feature of this article is that the results presented here are easily obtained using a generalized version of the Bochner technique due to theorems on the connection between the geometry of a complete Riemannian manifold and the global behavior of its subharmonic, superharmonic, and convex functions.

Keywords

• Bochner technique
• Riemannian and Kähler manifolds
• conformal diffeomorphism
• Liouville-type theorem
• scalar curvature
• paracomplex structure