A Simple Introduction to Complex Manifolds
The material discussed at the conference consisted of two applications of Kahler differential geometry nonlinear σ-models [1,2]. Since this material will be published in the standard literature, there is little point in interesting it again here. However, in the course of our work we found that Kahler geometry is a beautiful subject not well-known to most theoretical physicists and the essential part not as accessible as one might hope from the many mathematical textbooks. Kahler geometry not only has applications in supersymmetric σ-models, as was shown first by Zumino  and then in our work, but also in quantum gravity where every self-dual gravitational instantation is a Kahler manifold .
KeywordsComplex Manifold Parallel Transport Holonomy Group Mathematics Text Real Manifold
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