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Sasaki manifolds with positive transverse orthogonal bisectional curvature
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Hong Huang
Published/Copyright:
October 6, 2015
Abstract
In this short note we show the following result: Let (M2n+1, g) with n ≥ 2 be a compact Sasaki manifold with positive transverse orthogonal bisectional curvature. Then π1(M) is finite, and the universal cover of (M2n+1, g) is isomorphic to a simple metric on a weighted Sasaki sphere.We also get some results in the case of nonnegative transverse orthogonal bisectional curvature under some additional conditions. This extends recent work of He and Sun. The proof uses the Sasaki-Ricci flow.
Keywords: Sasaki manifolds; positive transverse orthogonal bisectional curvature; Sasaki-Ricci flow; maximum principle
Received: 2013-7-25
Revised: 2013-11-10
Published Online: 2015-10-6
Published in Print: 2015-10-1
© 2015 by Walter de Gruyter Berlin/Boston
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Keywords for this article
Sasaki manifolds;
positive transverse orthogonal bisectional curvature;
Sasaki-Ricci flow;
maximum principle
Articles in the same Issue
- Frontmatter
- Danzer’s configuration revisited
- Sasaki manifolds with positive transverse orthogonal bisectional curvature
- Real open books and real contact structures
- Locally Monge–Ampère parabolic foliations
- Gradient estimates for the heat equation under the Ricci-harmonic map flow
- The Log-Convex Density Conjecture and vertical surface area in warped products
- Further properties of the Bergman spaces of slice regular functions
- Constructions of complete sets
- The Euclidean distortion of generalized polygons
- On the geometrical properties of solvable Lie groups
- Another proof of the Beckman–Quarles theorem
