Kähler Reduction of Metrics with Holonomy G2
By V. Apostolov, S. Salamon. 2003
71 citations recorded by the source corpus.
A torsion-free G2 structure admitting an infinitesimal isometry such that the quotient is a Kähler manifold is shown to give rise to a 4-manifold equipped with a complex symplectic structure and a 1-parameter family of functions and 2-forms linked by second order equations. Reversing the process in various special cases leads to the construction of explicit metrics with holonomy equal to G2.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/b0250ca97074f60f39000ddb0040768128170a9e
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Hamiltonian Symmetries and Reduction in Generalized Geometry (2005, background): “, etc, the various reductions were considered as well. Because of the limited scope of this paper, we only mention some recent developements of these, from which more references can be found: K¨ahler [26, 27, 28, 29, 6], hyper-K¨ahler [8, 52, 49], contact [2, 17, 57], Sasakian [21, 16], Vaisman stru”
- Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “lete examples of explicit G2 holonomy metrics on non-compact manifolds were obtained by Salamon [Sal04]. G2 holonomy manifolds with isometric circle actions were investigated by Apostolov and Salamon [AS04]. The first compact examples are due to the ground breaking work of Joyce [Joy96b]. 9. Geometri”