Some Applications of Variational Calculus in Hermitian Geometry

Abstract

Variational methods have long been regarded as the mathematical foundation of both classical and quantum mechanics, and continue to supply much of the impetus of modern symplectic topology and geometry. Their application in Hermitian geometry is a more recent development, though of comparable importance. The following partial survey will set out to expose their role specifically on the theory of Hermitian-Einstein vector bundles, and in those aspects of conformal field theory which involve deformations of complex structure.