Generalized complex and paracomplex structures on product manifolds

Abstract

On a product manifold (Mr), we consider four geometric structures compatible with r, e.g. hyper-paracomplex or bi-Lagrangian, and define distinguished generalized complex or paracomplex structures on M, which interpolate between some pairs of them. We study the twistor bundles whose smooth sections are these new structures, obtaining the typical fibers as homogeneous spaces of classical groups. Also, we give examples of product manifolds admitting some of these new structures.

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Correspondence to Marcos Salvai.

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This work was supported by Consejo Nacional de Investigaciones Científicas y Técnicas, and Secretaría de Ciencia y Técnica de la Universidad Nacional de Córdoba.

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Fernández-Culma, E.A., Godoy, Y. & Salvai, M. Generalized complex and paracomplex structures on product manifolds. RACSAM 114, 154 (2020). https://doi.org/10.1007/s13398-020-00887-3

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Keywords

  • Generalized complex structure
  • Interpolation
  • Twistor bundle
  • Paracomplex manifold
  • Product structure

Mathematics Subject Classification

  • 22F30
  • 22F50
  • 53B30
  • 53B35
  • 53C15
  • 53C56
  • 53D05