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Soft Restrictions on Positively Curved Riemannian Submersions

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Abstract

We bound the dimension of the fiber of a Riemannian submersion from a positively curved manifold in terms of the dimension of the base of the submersion and either its conjugate radius or the length of its shortest closed geodesic.

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Acknowledgments

Both authors were supported by Research Grants MTM2011-22612 from the Ministerio de Ciencia e Innovación (MCINN) and MINECO: ICMAT Severo Ochoa Project SEV-2011-0087; the first author was also supported by FPI Grant BES-2012-053704. The authors would like to thank F. Galaz-García for helpful comments, and P. Piccione and W. Ziller for letting us know about references [2, 5] respectively.

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  1. Department of Mathematics, Universidad Autónoma de Madrid, and ICMAT CSIC-UAM-UCM-UC3M, Madrid, Spain

    David González-Álvaro & Luis Guijarro

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  1. David González-Álvaro
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  2. Luis Guijarro
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Correspondence to Luis Guijarro.

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González-Álvaro, D., Guijarro, L. Soft Restrictions on Positively Curved Riemannian Submersions. J Geom Anal 26, 1442–1452 (2016). https://doi.org/10.1007/s12220-015-9596-4

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  • DOI: https://doi.org/10.1007/s12220-015-9596-4

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