Mathematics

Mixed volume forms and complex equation of Monge–Ampere type on a torus

V. N. Kokarev

Dept. of Algebra and Geometry, Samara State University, Samara, 443011, Russia

Abstract: In this article a generalization of a Calabi problem is considered. In the analytical treatment it leads to the complex Monge–Ampere equation on Kähler manifold containing the mixed discriminant of the given and retrieved metrics. For the case when Kähler manifold is a flat complex torus, sufficient conditions for solvability are obtained.

Keywords: Kähler manifold, Monge–Ampere equation.

UDC: 514.772

Received: 06.07.2009
Revised: 06.07.2009