The affine quasi-Einstein Equation for homogeneous surfaces
Miguel Brozos-V\'azquez, Eduardo Garc\'ia-R\'io, Peter Gilkey and, Xabier Valle-Regueiro
TL;DR
This paper investigates the affine quasi-Einstein Equation on homogeneous surfaces and explores its implications for constructing new conformally Einstein and Einstein manifolds via Riemannian extensions and warped products.
Contribution
It introduces new methods for generating Einstein and conformally Einstein manifolds from affine quasi-Einstein equations on homogeneous surfaces.
Findings
New half conformally flat generalized quasi-Einstein neutral signature (2,2) manifolds
Construction of conformally Einstein manifolds
Generation of new Einstein manifolds through warped products
Abstract
We study the affine quasi-Einstein Equation for homogeneous surfaces. This gives rise through the modified Riemannian extension to new half conformally flat generalized quasi-Einstein neutral signature manifolds, to conformally Einstein manifolds and also to new Einstein manifolds through a warped product construction.
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