Complex manifolds without potential theory pdf

Complex structure on the six dimensional sphere from a. Complex analytic and differential geometry institut fourier. Existence of a complex structure on the 6 dimensional sphere is proved in this paper. Complex manifolds without potential theory springerlink. Geometric pluripotential theory on k ahler manifolds. The heart of the book is devoted to a proof of the main properties of these operators which have been playing a significant role in various areas of mathematics such as complex geometry, topological quantum field theory, integrable systems, and the study of links. Narasimhan no part of this book may be reproduced in any form by print, micro. Based on notes taken by james morrow from lectures given by kunihiko kodaira at stanford university in 19651966, the book gives the original proof of the kodaira embedding theorem, showing that the restricted class of kahler manifolds called hodge manifolds is. There is no question that complex analysis is a corner stone of the analysis education at every university and each area of mathematics requires at least some knowledge of it. Potential obstructions to the possibility of patching are measured by. Simple to complex with some numerical computations, was completed by mr. Chern, complex manifolds without potential theory, second edition, springerverlag, 1979.

From holomorphic functions to complex manifolds graduate. However, for functions u with dux 0, there is no natural definition of. Finite energy pluripotential theory accommodates the variational theory of equations of complex mongeamp ere type arising in k ahler geometry. In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in c n, such that the transition maps are holomorphic the term complex manifold is variously used to mean a complex manifold in the sense above which can be specified as an integrable complex manifold, and an almost complex manifold.

However, many mathematicians never take more than an. Theorems 1 and 4 below extend without any changes to quasiregular maps of surfaces. It is known 7,9 that the model cp1 is equivalent to the o3 q model but the connection has not been made explicit in terms of o2 supersymmetry. On geometric quantization of compact, complex manifolds. The purpose of this paper is to develop an intrinsic potential theory. There are surprisingly rich properties of these holomorphic functions. Pdf download complex manifolds without potential theory free. Complex manifolds lecture notes based on the course by lambertus van geemen a. A concise course in complex analysis and riemann surfaces. With an appendix on the geometry of characteristic classes universitext on free shipping on qualified orders.

Complex manifolds without potential theory with an. All of this structure is reflected in a rich theory of geometric and topological invariants. A good introduction to the theory of complex manifolds, a subject that is far deeper than just smooth manifold theory with the word \smooth replaced by. Morozov and perelomov, string theory and complex geometry, phys. Geometry of characteristic classes is a very neat and profound introduction to the. The proof is based on reinterpreting a hypothetical complex structure as a classical ground state of a yangmillshiggslike theory on s6. Complex manifolds stefan vandoren1 1 institute for theoretical physics and spinoza institute utrecht university, 3508 td utrecht, the netherlands s. The ones marked may be different from the article in the profile. Pdf complex and hermitian structures on a vector space. Sidharth kshatriya under my guidance during the academic year 20062007.

M we will denote by t x and t x the tangent and cotangent spaces respectively. Potential theory on almost complex manifolds numdam. Demailly, complex analytic and differential geometry pdf. Potential theory on almost complex manifolds department. Complex manifolds and hermitian differential geometry. The differential geometrical methods of this theory were developed essentially under the influence of professor s. These notes grew out of a course called complex manifolds and hermitian differential. Namely, they make either the complex numbers, in which case n 2 and there is a single complex structure j, or the quaternions, in which case n 2 and thre are three possible imaginary units j1,j2,j3. Potential theory on almost complex manifolds article pdf available in annales institut fourier 651 july 2011 with 47 reads how we measure reads. The differential geometrical methods of this theory were developed essentially under the. Pdf we introduce the notion of a special complex manifold. With an appendix on the geometry of characteristic classes, second edition universitext. Math 549 geometric structures spring 2004 suggested reading books about complex manifolds with the exception of m, which can be downloaded from the internet, these books are or soon should be on reserve in the math research library.

The authors intention is to introduce the reader in a simple way to the most important branches and methods in the theory of several complex variables. Subharmonic functions are an essential tool of harmonic analysis and potential theory. I certify that this is an original project report resulting from the work completed during this period. Its brief history and its future personal perspective shingtung yau once complex number is introduced as a. A classical invitation to algebraic numbers and class fields curtis. Cohomology and hodge theory on symplectic manifolds. With an appendix on the geometry of characteristic classes universitext on. Recently it has been discovered that many of the potential spaces involved have a rich metric geometry, e ectively turning the. The deformation theory of almost complex structures is described by the kodairaspencer theory which we note, is also relevant to the topological typeb string theory 10.

Harmonic forms and hodge theory on riemannian manifolds. This classical vacuum solution is then constructed by fourier expansion dimensional reduction from the obvious one of a similar theory. Chern, complex manifolds without potential theory 4. You can read online complex manifolds without potential theory here in pdf, epub, mobi or docx formats. Chern, complex manifolds without potential theory, new york, springerverlag, 1979. Almostcomplex and hypercomplex manifolds are considered in this paper from the point of view of complex analysis and potential theory. 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. Given a complex manifold x, we can think about xwithout its complex structure. The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and. These functions are defined classically by requiring that the restriction to each pseudoholomorphic curve is. Mathematical methods in field theory and complex analytic varieties 1971. Math 545 topology and geometry of manifolds winter 2000 suggestions for further reading.

Complex manifolds without potential theory chern s. If the complex manifold m may be covered by a bounded homogeneous domain in cn then it can be decomposed into a product of complex manifolds diffeomorphic to biquotient spaces r\gk where g is a noncompact simple lie group with a trivial center, k is a maximal connected compact lie subgroup of g and r is a subgroup of g acting in a free. The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. Pseudoholomorphic curves on almost complex manifolds have been much more intensely studied than their dual objects, the plurisubharmonic functions. Complex manifolds without potential theory eells 1980. Recently chern proposed 5 that noneof the almost complex structures. Math 545 topology and geometry of manifolds winter 2000. Shiingshen chern, complex manifolds without potential theory springerverlag press, 1995 isbn 0387904220, isbn 3540904220.