Complete manifolds with nonnegative curvature operator
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- by Lei Ni and Baoqiang Wu PDF
- Proc. Amer. Math. Soc. 135 (2007), 3021-3028
Abstract:
In this short note, as a simple application of the strong result proved recently by Böhm and Wilking, we give a classification on closed manifolds with $2$-nonnegative curvature operator. Moreover, by the new invariant cone constructions of Böhm and Wilking, we show that any complete Riemannian manifold (with dimension $\ge 3$) whose curvature operator is bounded and satisfies the pinching condition $R\ge \delta \frac {\operatorname {tr}(R)}{2n(n-1)} \mathrm {I}>0$, for some $\delta >0$, must be compact. This provides an intrinsic analogue of a result of Hamilton on convex hypersurfaces.References
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Additional Information
- Lei Ni
- Affiliation: Department of Mathematics, University of California at San Diego, La Jolla, California 92093
- MR Author ID: 640255
- Email: lni@math.ucsd.edu
- Baoqiang Wu
- Affiliation: Department of Mathematics, Xuzhou Normal University, Xuzhou, Jiangsu, People’s Republic of China
- Email: wubaoqiang@xznu.edu.cn
- Received by editor(s): June 22, 2006
- Received by editor(s) in revised form: August 16, 2006
- Published electronically: November 29, 2006
- Additional Notes: The first author was supported in part by NSF Grants and an Alfred P. Sloan Fellowship
- Communicated by: Jon G. Wolfson
- © Copyright 2006 by the authors
- Journal: Proc. Amer. Math. Soc. 135 (2007), 3021-3028
- MSC (2000): Primary 58J35
- DOI: https://doi.org/10.1090/S0002-9939-06-08872-1
- MathSciNet review: 2511306