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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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Volume 16, Issue 2

Issues

On spherical submanifolds with finite type spherical Gauss map

Burcu Bektas
  • Istanbul Technical University, Faculty of Science and Letters, Department of Mathematics, 34469 Maslak, Istanbul, Turkey
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/ Uğur Dursun
Published Online: 2016-04-16 | DOI: https://doi.org/10.1515/advgeom-2016-0005

Abstract

Chen and Lue (2007) initiated the study of spherical submanifolds with finite type spherical Gauss map. In this paper, we firstly prove that a submanifold Mn of the unit sphere Sm−1 has non-mass-symmetric 1-type spherical Gauss map if and only if Mn is an open part of a small n-sphere of a totally geodesic (n + 1)- sphere Sn+1 . Sm−1. Thenwe show that a non-totally umbilical hypersurfaceM of Sn+1 with nonzero constant mean curvature in Sn+1 has mass-symmetric 2-type spherical Gauss map if and only if the scalar curvature curvature of M is constant. Finally, we classify constant mean curvature surfaces in S3 with mass-symmetric 2-type spherical Gauss map.

Keywords: Finite type map; spherical Gauss map; mean curvature; isoparametric hypersurface

About the article

Received: 2014-09-12

Published Online: 2016-04-16

Published in Print: 2016-04-01


Citation Information: Advances in Geometry, Volume 16, Issue 2, Pages 243–251, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2016-0005.

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Citing Articles

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[1]
Burcu Bektaş, Elif Özkara Canfes, and Uğur Dursun
Mathematische Nachrichten, 2017
[2]
Burcu Bektaş, Elif Özkara Canfes, and Uğur Dursun
Results in Mathematics, 2017, Volume 71, Number 3-4, Page 867

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