Open Access
March 2010 Deformations of generalized complex generalized Kahler structures
Ryushi Goto
J. Differential Geom. 84(3): 525-560 (March 2010). DOI: 10.4310/jdg/1279114300


In this paper we obtain a stability theorem of generalized Kähler structures with one pure spinor under small deformations of generalized complex structures. (This is analogous to the stability theorem of Kähler manifolds by Kodaira-Spencer.) We apply the stability theorem to a class of compact Kähler manifolds which admits deformations to generalized complex manifolds and obtain non-trivial generalized Kähler structures on Fano surfaces and toric Kähler manifolds. In particular, we show that every nonzero holomorphic Poisson structure on a Kähler manifold induces deformations of non-trivial generalized Kähler structures.


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Ryushi Goto. "Deformations of generalized complex generalized Kahler structures." J. Differential Geom. 84 (3) 525 - 560, March 2010.


Published: March 2010
First available in Project Euclid: 14 July 2010

zbMATH: 1201.53085
MathSciNet: MR2669364
Digital Object Identifier: 10.4310/jdg/1279114300

Rights: Copyright © 2010 Lehigh University

Vol.84 • No. 3 • March 2010
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