Kahler manifolds are a special class of complex manifolds. These functions are defined classically by requiring that the restriction to each pseudoholomorphic curve is subharmonic. Complex manifolds and hermitian differential geometry. With an appendix on the geometry of characteristic classes, second edition universitext. First, by using operators from hodge theory on compact k\ahler manifold, we present a closed explicit extension formula for holomorphic canonical forms in different complex structures. A classical invitation to algebraic numbers and class fields curtis. Chern, complex manifolds without potential theory springer ver. The differential geometrical methods of this theory were developed essentially under the influence of professor s. The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. Yangmills, complex structures and cherns last theorem. They are necessarily of even dimension, say 2n, and allow for a collection of charts u j,z j that are one to one maps of the corresponding u j to cn such that for every nonempty. Model theory of compact complex manifolds with an automorphism. For an example with a local but not global potential, consider cpn with the standard fubinistudy.
The purpose of this paper is to develop an intrinsic potential theory on a general. These notes grew out of a course called complex manifolds and hermitian. Pdf potential theory on almost complex manifolds researchgate. Complex manifolds without potential theory with an appendix on.
Pseudoholomorphic curves on almost complex manifolds have been much more intensely studied than their dual objects, the plurisubharmonic functions. Potential theory on almost complex manifolds numdam. Potential theory on almost complex manifolds article pdf available in annales institut fourier 651 july 2011 with 48 reads how we measure reads. Complex manifolds without potential theory with an. Pdf pseudoholomorphic curves on almost complex manifolds. Complex manifolds without potential theory springerlink. However, for functions u with dux 0, there is no natural definition of. With an appendix on the geometry of characteristic classes universitext on.
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