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Geometric structures on loop and path spaces

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Abstract

The loop space associated to a Riemannian manifold admits a quasisymplectic structure (that is, a closed 2-form which is non-degenerate up to a finite-dimensional kernel). We show how to construct a compatible almost-complex structure. Finally conditions to have contact structures on loop spaces are studied.

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040, Madrid, Spain

    Vicente Muñoz & Francisco Presas

  2. Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Serrano 113bis, 28006, Madrid, Spain

    Francisco Presas

Authors
  1. Vicente Muñoz
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  2. Francisco Presas
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Correspondence to Vicente Muñoz.

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Muñoz, V., Presas, F. Geometric structures on loop and path spaces. Proc Math Sci 120, 417–428 (2010). https://doi.org/10.1007/s12044-010-0036-x

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  • DOI: https://doi.org/10.1007/s12044-010-0036-x

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