Complex Connections with Trivial Holonomy

  • Adrian Andrada
  • Maria Laura Barberis
  • Isabel Dotti
Chapter
Part of the Progress in Mathematics book series (PM, volume 306)

Abstract

Given an almost complex manifold (M, J), we study complex connections with trivial holonomy such that the corresponding torsion is either of type (2, 0) or of type (1, 1) with respect to J. Such connections arise naturally when considering Lie groups, and quotients by discrete subgroups, equipped with bi-invariant and abelian complex structures.

Keywords

Complex flat connections Abelian connections Complex parallelizable manifolds 

Notes

Acknowledgments

We dedicate this article to Joe Wolf, whose work has inspired the research of many mathematicians in the broad field of Differential Geometry and Lie Theory. We are grateful for his important contribution to the development of our mathematics department.

The authors were partially supported by CONICET, ANPCyT and SECyT-UNC (Argentina).

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Adrian Andrada
    • 1
  • Maria Laura Barberis
    • 1
  • Isabel Dotti
    • 1
  1. 1.FaMAF-CIEMUniversidad Nacional de CórdobaCórdobaArgentina

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