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Nonnegatively curved vector bundles with large normal holonomy groups


Author: Kristopher Tapp
Journal: Proc. Amer. Math. Soc. 136 (2008), 295-300
MSC (2000): Primary 53Cxx
DOI: https://doi.org/10.1090/S0002-9939-07-08983-6
Published electronically: October 12, 2007
MathSciNet review: 2350416
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Abstract: When $ B$ is a biquotient, we show that there exist vector bundles over $ B$ with metrics of nonnegative curvature whose normal holonomy groups have arbitrarily large dimension.


References [Enhancements On Off] (What's this?)

  • 1. K. Grove and W. Ziller, Curvature and symmetry of Milnor spheres, Annals of Mathematics. 152 (2000), 331-336. MR 1792298 (2001i:53047)
  • 2. G. Perelman, Proof of the soul conjecture of Cheeger and Gromoll, J. Differential Geom. 40 (1994), 209-212. MR 1285534 (95d:53037)
  • 3. M. Strake, A splitting theorem for open nonnegatively curved manifolds, Manuscripta Math. 61, 315-325. MR 949821 (89g:53066)
  • 4. K. Tapp, Conditions of nonnegative curvature on vector bundles and sphere bundles, Duke Math. J. 116 (2003), no. 1, 77-101. MR 1950480 (2004b:53045)
  • 5. K. Tapp, Volume growth and holonomy in nonnegative curvature, Proc. Amer. Math. Soc. 127 (1999), no. 10, pp. 3035-3041. MR 1605945 (2000a:53053)
  • 6. K. Tapp, Rigidity for nonnegatively curved metrics on $ S^2\times\R^3$, Annals of Global Analysis and Geometry 25 (2004), 43-58.
  • 7. B. Wilking, A contribution to the structure of complete open manifolds of nonnegative curvature, undergraduate thesis, Munster, 1995, unpublished.
  • 8. B. Wilking, A duality theorem for Riemannian foliations in nonnegative sectional curvature, preprint.
  • 9. B. Wilking, Manifolds with positive sectional curvature almost everywhere, Invent. Math. 148 (2002), 117-141. MR 1892845 (2003a:53049)
  • 10. D. Yang, On complete metrics of nonnegative curvature on $ 2$-plane bundles, Pacific J. of Math., Vol. 171, No. 2, 1995. MR 1372245 (96k:53034)
  • 11. J.W. Yim, Space of souls in a complete open manifold of nonnegative curvature, J. Differential Geom. 32 (1990), 429-455. MR 1072913 (91j:53023)

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Additional Information

Kristopher Tapp
Affiliation: Department of Mathematics and Computer Science, Suffolk University, Fenton Building, Room 621, 32 Derne St., Boston, Massachusetts 02114
Email: ktapp@mcs.suffolk.edu

DOI: https://doi.org/10.1090/S0002-9939-07-08983-6
Keywords: Nonnegative curvature, biquotient, holonomy
Received by editor(s): April 21, 2006
Received by editor(s) in revised form: October 23, 2006
Published electronically: October 12, 2007
Additional Notes: The author was supported in part by NSF grant DMS–0303326.
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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