Non-degenerate homogeneous ε-Kähler and ε-quaternion Kähler structures of linear type

2013/11/13 by Ignacio Luján, Andrew Swann, Luján, Ignacio +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1311.3072

29 pages

arxiv created 2013/11/13 · arxiv updated 2013/11/14

Abstract

We study the class of non-degenerate homogeneous structures of linear type in the pseudo-Kähler, para-Kähler, pseudo-quaternion Kähler and para-quaternion Kähler cases. We show that these structures characterize spaces of constant holomorphic, para-holomorphic, quaternion and para-quaternion sectional curvature respectively. In addition the corresponding homogeneous models are computed, exhibiting the relation between these kind of structures and the incompleteness of the metric.

Related

• Homogeneous structures of linear type on ε-Kähler and ε-quaternion Kähler manifolds
• Homogeneous quaternionic Kaehler structures and quaternionic hyperbolic space
• Strongly degenerate homogeneous pseudo-Kähler structures of linear type and complex plane waves
• A new construction of homogeneous quaternionic manifolds and related geometric structures
• Homogeneous HKT and QKT manifolds