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Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 17–46 | Cite as

Generalized metrics and generalized twistor spaces

  • Johann DavidovEmail author
Article
  • 48 Downloads

Abstract

The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry à la Hitchin). The generalized twistor space associated to such a manifold is defined as the bundle of generalized complex structures on the tangent spaces of the manifold compatible with the given generalized metric. This space admits natural generalized almost complex structures whose integrability conditions are found in the paper. An interesting feature of the generalized twistor spaces discussed in it is the existence of intrinsic isomorphisms.

Keywords

Generalized complex structures Twistor spaces 

Mathematics Subject Classification

53D18 53C28 

Notes

Acknowledgements

I would like to thank the referee whose remarks and comments helped to improve the final version of the paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

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