Sasaki manifolds with positive transverse orthogonal bisectional curvature

2013/01/07 by Hong Huang, Huang, Hong · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1301.1229

openalex publication_date 2013/01/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this short note we show the following result: Let (M²ⁿ⁺¹,g) (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 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 Sasaki-Ricci flow.

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• New curvature characterization for the weighted Sasaki sphere

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