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manuscripta mathematica

, Volume 151, Issue 3–4, pp 453–468 | Cite as

Interpolation of geometric structures compatible with a pseudo Riemannian metric

  • Edison Alberto Fernández-Culma
  • Yamile GodoyEmail author
  • Marcos Salvai
Article
  • 56 Downloads

Abstract

Let (M, g) be a pseudo Riemannian manifold. We consider four geometric structures on M compatible with g: two almost complex and two almost product structures satisfying additionally certain integrability conditions. For instance, if r is paracomplex and symmetric with respect to g, then r induces a pseudo Riemannian product structure on M. Sometimes the integrability condition is expressed by the closedness of an associated two-form: if j is almost complex on M and \(\omega (x,y)=g(jx,y)\) is symplectic, then M is almost pseudo Kähler. Now, product, complex and symplectic structures on M are trivial examples of generalized (para)complex structures in the sense of Hitchin. We use the latter in order to define the notion of interpolation of geometric structures compatible with g. We also compute the typical fibers of the twistor bundles of the new structures and give examples for M a Lie group with a left invariant metric.

Mathematics Subject Classification

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Edison Alberto Fernández-Culma
    • 1
  • Yamile Godoy
    • 1
    Email author
  • Marcos Salvai
    • 1
  1. 1.CIEM-FaMAFConicet - Universidad Nacional de CórdobaCórdobaArgentina

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