Generalized geometry and the Hodge decomposition

Details Generalized geometry and the Hodge decomposition Generalized geometry and the Hodge decomposition

2004-09-07

arxiv.org/abs/math/0409093v1

Mathematics

Differential Geometry

Lecture at the String Theory and Geometry workshop, August 2004, Oberwolfach. 7 pages

Scientific paper

In this lecture, we review some of the concepts of generalized geometry, as
introduced by Hitchin and developed in the speaker's thesis. We also prove a
Hodge decomposition for the twisted cohomology of a compact generalized
K\"ahler manifold, as well as a generalization of the $dd^c$-lemma of K\"ahler
geometry.

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