Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Nonnegatively curved vector bundles with large normal holonomy groups

Author(s): Kristopher Tapp
Journal: Proc. Amer. Math. Soc. 136 (2008), 295-300.
MSC (2000): Primary 53Cxx
Posted: October 12, 2007
MathSciNet review: 2350416
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

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:

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contribution to the structure of complete open manifolds of nonnegative curvature, undergraduate thesis, Munster, 1995, unpublished.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)


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53Cxx

Retrieve articles in all Journals with MSC (2000): 53Cxx


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: 10.1090/S0002-9939-07-08983-6
PII: S 0002-9939(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
Posted: October 12, 2007
Additional Notes: The author was supported in part by NSF grant DMS--0303326.
Communicated by: Jon G. Wolfson
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia