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Rigidity of flat sections on non-negatively curved pullback submersions

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Abstract

We give a geometric obstruction to the non-negativity of the sectional curvature in the total spaces of Riemannian submersions defined as pullbacks. Applications of this obstruction to several examples are given.

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Authors and Affiliations

  1. Departamento de Matemática, Setor de Ciências Exatas, Centro Politécnico, UFPR, Caixa Postal 019081, Curitiba, PR, CEP 81531-990, Brazil

    C. Durán & L. D. Sperança

  2. IMECC - Unicamp, Rua Sérgio Buarque de Holanda, Cidade Universitária, Campinas, 13083-859, Brazil

    L. D. Sperança

Authors
  1. C. Durán
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  2. L. D. Sperança
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Corresponding author

Correspondence to C. Durán.

Additional information

L. D. Sperança was partially supported by FAPESP, Grant Numbers 2009/07953-8 and 2012/25409-6.

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Durán, C., Sperança, L.D. Rigidity of flat sections on non-negatively curved pullback submersions. manuscripta math. 147, 511–525 (2015). https://doi.org/10.1007/s00229-015-0731-0

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  • DOI: https://doi.org/10.1007/s00229-015-0731-0

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