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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. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Stein manifolds of nonnegative curvature

Xiaoyang Chen
Published Online: 2016-11-23 | DOI: https://doi.org/10.1515/advgeom-2016-0025

Abstract

Let X bea Stein manifold with an anti-holomorphic involution τ and nonempty compact fixed point set Xτ. We show that X is diffeomorphic to the normal bundle of Xτ provided that X admits a complete Riemannian metric g of nonnegative sectional curvature such that τ* g = g.

Keywords: Stein manifold; nonnegative curvature; soul theorem

MSC 2010: Primary 53C20; 53C24; Secondary 53C21; 53C25

Communicated by: P. Eberlein

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About the article

Received: 2016-01-09

Received: 2016-05-17

Published Online: 2016-11-23

Published in Print: 2016-11-01


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2016-0025.

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