Solutions to the affine quasi-Einstein equation for homogeneous surfaces-Reference-Cited by-同舟云学术

Solutions to the affine quasi-Einstein equation for homogeneous surfaces

Published:2020-07-01 Issue:3 Volume:20 Page:413-432
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Brozos-Vázquez M.¹,García-Río E.²,Gilkey P.³,Valle-Regueiro X.²

Affiliation:

1. Universidade da Coruña, Differential Geometry and its Applications Research Group, Escola Politécnica Superior , 15403 , Ferrol , Spain

2. Faculty of Mathematics , University of Santiago de Compostela , 15782 , Santiago de Compostela , Spain

3. Mathematics Department , University of Oregon , Eugene , OR 97403-1222 , USA

Abstract

Abstract We examine the space of solutions to the affine quasi–Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitons, conformally Einstein metrics, and warped product Einstein manifolds using the modified Riemannian extension, we provide very explicit descriptions of these solution spaces. We use the dimension of the space of affine Killing vector fields to structure our discussion as this provides a convenient organizational framework.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2020-0011/pdf

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