Reduction of generalized Calabi-Yau structures. (English) Zbl 1186.37064

Nitta, Yasufumi

J. Math. Soc. Japan 59, No. 4, 1179-1198 (2007).

Generalized Calabi-Yau structures are geometrical structures defined by differential forms with the aim of generalizing the concept of Calabi-Yau structures and symplectic structures. These aspects are discussed in Section 2 of the paper. In the next section, the author uses the notion of generalized moment maps for a compact Lie group action on a generalized Clabi-Yau manifold to construct a Calabi-Yau structure on the reduced space. It is shown that the reduced generalized Calabi-Yau structure is unique. In the last section, the author proves the Duistermaat-Heckman formula for the corresponding volume form, for a Hamiltonian, effective torus action on a generalized Calabi-Yau manifold of constant type.

Reviewer: Ioan Bucataru (Iaşi)

MSC:

37J15	Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)
14J32	Calabi-Yau manifolds (algebro-geometric aspects)
53D20	Momentum maps; symplectic reduction
53C55	Global differential geometry of Hermitian and Kählerian manifolds

Keywords:

generalized Calabi-Yau structures; generalized moment map; Duistermaat-Heckman formula