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Ricci Solitons and Geometry of Four-dimensional Non-reductive Homogeneous Spaces

Published online by Cambridge University Press:  20 November 2018

Giovanni Calvaruso  and
Anna Fino
Giovanni Calvaruso
Affiliation:
Dipartimento di Matematica “E. De Giorgi”, Universitá del Salento, Prov. Lecce-Arnesano, 73100 Lecce, Italy email: [email protected]
Anna Fino
Affiliation:
Dipartimento di Matematica, Universitá di Torino, Via Carlo Alberto 10, 10123 Torino, Italy email: [email protected]
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Abstract

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We study the geometry of non-reductive four-dimensional homogeneous spaces. In particular, after describing their Levi-Civita connection and curvature properties, we classify homogeneous Ricci solitons on these spaces, proving the existence of shrinking, expanding and steady examples. For all the non-trivial examples we find, the Ricci operator is diagonalizable.

Keywords

53C2153C5053C25non-reductive homogeneous spacespseudo-RiemannianmetricsRicci solitonsEinsteinlike metrics
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 4 , 01 August 2012 , pp. 778 - 804
Copyright
Copyright © Canadian Mathematical Society 2012

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