Some Complex Quantum Manifolds and their Geometry

Details Some Complex Quantum Manifolds and their Geometry Some Complex Quantum Manifolds and their Geometry

1996-08-29

arxiv.org/abs/hep-th/9608188v1

Physics

High Energy Physics

High Energy Physics - Theory

Cargese lectures, July 1996, one figure, Full postscript available from http://theor1.lbl.gov/www/theorgroup/papers/39275.ps

Scientific paper

After recalling briefly some basic properties of the quantum group $GL_q(2)$, we study the quantum sphere $S_q^2$, quantum projective space $CP_q(N)$ and quantum Grassmannians as examples of complex (K\"{a}hler) quantum manifolds. The differential and integral calculus on these manifolds are discussed. It is shown that many relations of classical projective geometry generalize to the quantum case. For the case of the quantum sphere a comparison is made with A. Connes' method.

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