【摘要】
In a joint work with Josh Jordan, we study a Monge-Ampere equation of split type, which arises naturally in the study of Hermitian geometry of complex manifolds with split tangent bundles. The surface case has been studied by Beauville in algebraic geometry. Similar to the Kahler case, we pose the prescribing Bismut-Ricci problem and a Calabi type problem in this setting and solve them in dimension 2. As applications, we establish canonical metrics on two important type of class VII examples: primary Hopf surfaces and Inoue surfaces of type M.
