A canonical hyperkaehler metric on the total space of a cotangent bundle

TL;DR

This paper simplifies the construction of a canonical hyperkaehler metric on the cotangent bundle of a complex manifold and provides an explicit formula for Hermitian symmetric spaces.

Contribution

It streamlines the existing construction of hyperkaehler metrics and introduces an explicit formula for Hermitian symmetric spaces.

Findings

Explicit formula for hyperkaehler metric on Hermitian symmetric spaces

Simplified presentation of previous construction

Enhanced understanding of cotangent bundle geometries

Abstract

A canonical hyperkaehler metric on the total space $T^*M$ of a cotangent bundle to a complex manifold $M$ has been constructed recently by the author (see alg-geom/9710026). This paper presents the results of alg-geom/9710026 in a streamlined and simplified form. The only new result is an explicit formula obtained for the case when $M$ is an Hermitian symmetric space.