A Variational Approach to SKT and Balanced Metrics

Abstract

We investigate compact complex manifolds endowed with SKT or balanced metrics. In each case we define a new functional whose critical points are proved to be precisely the K\"ahler metrics, if any, on the manifold. As general manifolds of either type need not admit K\"ahler metrics, this provides an approach to new obstructions to K\"ahlerianity within these two families of metrics.