Conformal holomorphically projective mappings satisfying a certain initial condition

Abstract

In this paper we study conformal holomorphically projective mappings between conformal e-Kähler manifolds Kn=(M, g, F ) and Kn=( M, g, F ), i. e. diffeomorphisms f : M → M satisfying f = f1 o f2 o f3, where f1, f3 are conformal mappings and f2 is a holomorphically projective mapping between e-Kähler manifolds (i. e. Kähler, pseudo-Kähler and hyperbolic Kähler manifolds). Suppose that the initial condition f * g = k . g is satisfied at a point x0 ∈ M and that at this point the Weyl conformal tensor satisfies a certain inequality. We prove that the mapping f is then necessarily conformal. © 2013 Miskolc University Press.