1 results
Generalized Kähler–Einstein Metrics and Energy Functionals
-
- Journal:
- Canadian Journal of Mathematics / Volume 66 / Issue 6 / 01 December 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1413-1435
- Print publication:
- 01 December 2014
-
- Article
-
- You have access
- Export citation
-
In this paper, we consider a generalized Kähler–Einstein equation on a Kähler manifold
$M$. Using the twisted 
$\mathcal{K}$–energy introduced by Song and Tian, we show that the existence of generalized Kähler–Einstein metrics with semi–positive twisting (1, 1)–form 
$\theta$ is also closely related to the properness of the twisted $\mathcal{K}$-energy functional. Under the condition that the twisting form $\theta$ is strictly positive at a point or $M$ admits no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of generalized Kähler–Einstein metric implies a Moser–Trudinger type inequality.
