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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

IMPACT FACTOR 2018: 0.789

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Volume 15, Issue 4


Sasaki manifolds with positive transverse orthogonal bisectional curvature

Hong Huang
  • Corresponding author
  • School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, P.R. China
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Published Online: 2015-10-06 | DOI: https://doi.org/10.1515/advgeom-2015-0020


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

About the article

Received: 2013-07-25

Revised: 2013-11-10

Published Online: 2015-10-06

Published in Print: 2015-10-01

Citation Information: Advances in Geometry, Volume 15, Issue 4, Pages 409–413, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2015-0020.

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