Reduction of generalized Calabi-Yau structures
微分几何
2007-05-23 v2 辛几何
摘要
A generalized Calabi-Yau structure is a geometrical structure on a manifold which generalizes both the concept of the Calabi-Yau structure and that of the symplectic one. In view of a result of Lin and Tolman in generalized complex cases, we introduce in this paper the notion of a generalized moment map for a compact Lie group action on a generalized Calabi-Yau manifold and construct a reduced generalized Calabi-Yau structure on the reduced space. As an application, we show some relationship between generalized moment maps and the Bergman kernels, and prove the Duistermaat-Heckman formula for a torus action on a generalized Calabi-Yau manifold.
引用
@article{arxiv.math/0611341,
title = {Reduction of generalized Calabi-Yau structures},
author = {Yasufumi Nitta},
journal= {arXiv preprint arXiv:math/0611341},
year = {2007}
}
备注
14 pages, to appear in J. Math. Soc. Japan, Vol 59, no. 4(2007)