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Non-degenerate homogeneous \(\epsilon \)-Kähler and \(\epsilon \)-quaternion Kähler structures of linear type

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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.

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad Complutense de Madrid, Av. Complutense s/n, 28040, Madrid, Spain

    Ignacio Luján

  2. Department of Mathematics, Aarhus University, Ny Munkegade 118, Bldg 1530, 8000, Aarhus C, Denmark

    Andrew Swann

  3. CP3-Origins, Centre of Excellence for Cosmology and Particle Physics Phenomenology, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark

    Andrew Swann

Authors
  1. Ignacio Luján
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  2. Andrew Swann
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Correspondence to Ignacio Luján.

Additional information

Communicated by A. Constantin.

Partially supported by MINECO, Spain, under grant MTM2011-22528 and by the Danish Council for Independent Research, Natural Sciences.

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Luján, I., Swann, A. Non-degenerate homogeneous \(\epsilon \)-Kähler and \(\epsilon \)-quaternion Kähler structures of linear type. Monatsh Math 178, 113–142 (2015). https://doi.org/10.1007/s00605-015-0783-y

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  • DOI: https://doi.org/10.1007/s00605-015-0783-y

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