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- On the asymptotic expansion of the curvature of perturbations of the $L_{2}$ connection
Submitted manuscript, 613 KB, PDF document

- 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 language | English |
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Publisher | Aarhus University, Science and Technology |
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Number of pages | 87 |

Publication status | Published - 2013 |

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ID: 52589255