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An application of Bochner's technique to the deformations of the complex structure of $\mathbb C \mathbb P^n$

Author(s): Yong Ouyang
Journal: Proc. Amer. Math. Soc. 131 (2003), 3703-3709.
MSC (2000): Primary 32G05, 58J05
Posted: July 2, 2003
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Abstract: We consider the deformation of the complex structure of $\mathbb C \mathbb P^n$ . We show that a harmonic deformation on $\mathbb C \mathbb P^n$ equipped with the Fubini-Study metric is trivial if its supernorm is appropriately small.

References:

1.: Kunihiko Kodaira, J. Morrow, Complex manifolds, Holt, Rinehart and Winston, Inc., New York, 1971. MR 46:2080
2.: M. Kuranishi, New proof for the existence of locally complete families of complex structures, Proceedings of the Conference on Complex Analysis in Minneapolis, 1964. Berlin: Springer-Verlag, 1965, pp. 142-154. MR 31:768


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