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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bannai, Eiichi / 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 / Pasini, Antonio / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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1615-7168
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Volume 14, Issue 2

Issues

Generic properties of homogeneous Ricci solitons

L. F. Di Cerbo
Published Online: 2014-04-01 | DOI: https://doi.org/10.1515/advgeom-2013-0031

Abstract

We discuss the geometry of homogeneous Ricci solitons. After showing the nonexistence of compact homogeneous and non-compact steady homogeneous solitons, we concentrate on the study of left invariant Ricci solitons. We show that, in the unimodular case, the Ricci soliton equation does not admit solutions in the set of left invariant vector fields. We prove that a left invariant soliton of gradient type must be a Riemannian product with non-trivial Euclidean de Rham factor. As an application of our results we prove that any generalized metric Heisenberg Lie group is a non-gradient left invariant Ricci soliton of expanding type.

About the article

Published Online: 2014-04-01

Published in Print: 2014-03-01


Citation Information: Advances in Geometry, Volume 14, Issue 2, Pages 225–237, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2013-0031.

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©2014 by Walter de Gruyter Berlin/Boston. Copyright Clearance Center

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