On the asymptotic expansion of the curvature of perturbations of the $L_{2}$ connection

Research output: Book/anthology/dissertation/reportPh.D. thesisResearch

  • Amit De, Denmark
We establish that the Hitchin connection is a perturbation of the $L_{2}$-connection. We notice that such a formulation of the Hitchin connection does not necessarily require the manifold in question possessing a rigid family of Kähler structures. We then proceed to calculate the asymptotic expansion of general perturbations of the $L_{2}$-connection, and see when under certain assumptions such perturbations are flat and projectively flat. During the calculations we also found an asymptotic expansion of the projection operator $\pi_{\sigma}^{\left(k\right)}$ which projects onto the holomorphic sections of the k-th tensor of prequantum line bundle.
Original languageEnglish
PublisherAarhus University, Science and Technology
Number of pages87
Publication statusPublished - 2013

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