Metrics of Eguchi-Hanson types with the negative constant scalar curvature

TL;DR

This paper constructs two new types of Eguchi-Hanson metrics with negative scalar curvature, including a Kähler type and an ALH type with potentially negative total energy, expanding the understanding of such geometric structures.

Contribution

It introduces two novel classes of Eguchi-Hanson metrics with negative scalar curvature, one being Kähler and the other ALH with negative total energy.

Findings

Constructed Kähler Eguchi-Hanson metrics with negative scalar curvature

Developed ALH Eguchi-Hanson metrics with negative total energy

Expanded the catalog of explicit metrics with negative scalar curvature

Abstract

We construct two types of Eguchi-Hanson metrics with the negative constant scalar curvature. The type I metrics are K\"{a}hler. The type II metrics are ALH whose total energy can be negative.