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Properly discontinuous actions on Hilbert manifolds

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Abstract

In this article we study properly discontinuous actions on Hilbert manifolds giving new examples of complete Hilbert manifolds with nonnegative, respectively nonpositive, sectional curvature with infinite fundamental group. We also get examples of complete infinite dimensional Kähler manifolds with positive holomorphic sectional curvature and infinite fundamental group in contrastwith the finite dimensional case and we classify abelian groups acting linearly, isometrically and properly discontinuously on Stiefel manifolds. Finally, we classify homogeneous Hilbert manifolds with constant sectional curvature.

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Authors and Affiliations

  1. Università di Parma, Parma, Italy

    Leonardo Biliotti

  2. Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

    Francesco Mercuri

Authors
  1. Leonardo Biliotti
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  2. Francesco Mercuri
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Corresponding author

Correspondence to Leonardo Biliotti.

Additional information

The authors were partially supported by FIRB 2012 “Geometria differenziale e teoria geometrica delle functioni” grant RBFR12W1AQ003. The second author was partially supported by Fapesp and CNPq (Brazil).

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Biliotti, L., Mercuri, F. Properly discontinuous actions on Hilbert manifolds. Bull Braz Math Soc, New Series 45, 433–452 (2014). https://doi.org/10.1007/s00574-014-0057-7

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  • DOI: https://doi.org/10.1007/s00574-014-0057-7

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