Quasi-Einstein metrics on hypersurface families

TL;DR

This paper constructs quasi-Einstein metrics on specific hypersurface families, linking them to known gradient Kähler-Ricci solitons and Hermitian Einstein metrics, expanding the understanding of Einstein-like structures on complex manifolds.

Contribution

It introduces new quasi-Einstein metrics on circle bundle hypersurfaces over Fano, Kähler-Einstein manifolds, connecting them to existing gradient Kähler-Ricci solitons and Hermitian Einstein metrics.

Findings

Construction of quasi-Einstein metrics on hypersurface families.

Connection to gradient Kähler-Ricci solitons.

Relation to Hermitian, non-Kähler Einstein metrics.

Abstract

We construct quasi-Einstein metrics on some hypersurface families. The hypersurfaces are circle bundles over the product of Fano, K\"ahler-Einstein manifolds. The quasi-Einstein metrics are related to various gradient K\"ahler-Ricci solitons constructed by Dancer and Wang and some Hermitian, non-K\"ahler, Einstein metrics constructed by Wang and Wang on the same manifolds.