In this continuation of , we investigate the deformations of holomorphic Cartan geometries where the underlying complex manifold is allowed to move. The space of infinitesimal deformations of a flat holomorphic Cartan geometry is computed. We show that the natural forgetful map, from the infinitesimal deformations of a flat holomorphic Cartan geometry to the infinitesimal deformations of the underlying flat principal bundle on the topological manifold, is an isomorphism.
 I. Biswas and S. Dumitrescu, Generalized holomorphic Cartan geometries, European J. Math. 6 (special issue dedicated to the memory of Stefan Papadima) (2020), 661–680.10.1007/s40879-019-00327-6Search in Google Scholar
 R. D. Canary, D. B. A. Epstein and P. Green, Notes on notes of Thurston, Analytical and geometric aspects of hyperbolic space (Coventry/Durham, 1984), 3–92, London Math. Soc. Lecture Note Ser., 111, Cambridge Univ. Press, Cambridge, 1987.Search in Google Scholar
 C. Ehresmann, Sur les espaces localement homogènes, L’Enseign. Math.35 (1936), 317–333.Search in Google Scholar
 W. M. Goldman and J. J. Millson, The deformation theory of representations of fundamental groups of compact Kähler manifolds, Inst. Hautes Études Sci. Publ. Math.67 (1988), 43–96.10.1007/BF02699127Search in Google Scholar
 R. C. Gunning, On uniformization of complex manifolds: the role of connections, Princeton Univ. Press, 1978.Search in Google Scholar
 M. S. Raghunathan, Vanishing theorems for cohomology groups associate to discrete subgroups of semi-simple Lie groups, Osaka Math. Jour.3 (1966), 243–256, corrections ibid. 16, (1979), 295–299.Search in Google Scholar
 R. W. Sharpe, Di˙erential Geometry : Cartan’s Generalization of Klein’s Erlangen Program, Graduate Text Math., 166, Springer-Verlag, New York, Berlin, Heidelberg, 1997.Search in Google Scholar
 Y. Wakabayashi, Frobenius-Ehresmann structures and Cartan geometries in positive characteristic, arXiv:2109.02826.Search in Google Scholar
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