Complete manifolds with nonnegative curvature operator
By Lei Ni, Baoqiang Wu. 2006
54 citations recorded by the source corpus.
In this short note, as a simple application of the strong result proved recently by Bohm and Wilking, we give a classification on closed manifolds with 2-nonnegative curvature operator. Moreover, by the new invariant cone constructions of Bohm and Wilking, we show that any complete Riemannian manifold (with dimension > 3) whose curvature operator is bounded and satisfies the pinching condition R > δtr(R)/2n(n-1) I > 0, for some δ > 0, must be compact. This provides an intrinsic analogue of a result of Hamilton on convex hypersurfaces.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/f61a7ce019413d64c6c7876aec974d8bf804107c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Burkhard Wilking
- Lei Ni
- Nolan Wallach
- Huaihuo Cao
- Brett Kotschwar
- W. Wylie
- Peter Petersen
- Xiaodong Cao
In Geometry and Topology
- Burkhard Wilking
- Lei Ni
- Huaihuo Cao
- Brett Kotschwar
- W. Wylie
- Peter Petersen
- Xiaodong Cao
- Zhuhong Zhang
Citations in the corpus
- On a classification of the gradient shrinking solitons (2007, background): “t (M,g) is either Einstein or its Ricci curvature has constant rank n− 1 and with n− 1 identical nonzero eigenvalues. q.e.d. Remark 5.3. (1) The compactness part should be compared with the result in [NW], where under certain curvature operator pinching condition, the manifold is shown to be compact”
- Nonnegatively and Positively curved manifolds (2007, background): “It actually suffices to assume that the curvature operator of (M, g) is contained in C at all points, and in the interior of C at some point, cf. [Ni and Wu, 2006].”