Quasi-Einstein metrics on sphere bundles
Solomon Huang, Tommy Murphy, and Thanh Nhan Phan
TL;DR
This paper adapts existing methods to construct quasi-Einstein metrics on sphere bundles over Fano Kähler-Einstein manifolds, including cases with blown-down ends, expanding the understanding of such geometric structures.
Contribution
It introduces a new approach to find quasi-Einstein metrics on sphere bundles over specific complex manifolds, extending previous work to more general bundle configurations.
Findings
Constructed explicit quasi-Einstein metrics on sphere bundles
Extended methods to bundles with one blown-down end
Enhanced understanding of geometric structures on complex manifolds
Abstract
In this note we adapt the work of Hall to find quasi-Einstein metrics on sphere bundles over products of Fano Kaehler-Einstein manifolds, as well as bundles where only one end is blown down.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics