# Ricci-flat K\"ahler metrics on tangent bundles of rank-one symmetric spaces of compact type

## TL;DR

This paper explicitly describes all complete G-invariant Ricci-flat Kähler metrics on tangent bundles of rank-one symmetric spaces of compact type using associated vector-functions.

## Contribution

It provides a comprehensive explicit characterization of Ricci-flat Kähler metrics on tangent bundles of rank-one symmetric spaces, extending previous understanding.

## Key findings

- Complete classification of G-invariant Ricci-flat Kähler metrics
- Explicit formulas in terms of associated vector-functions
- Application to tangent bundles of rank-one symmetric spaces

## Abstract

We give an explicit description of all complete $G$-invariant Ricci-flat K\"ahler metrics on the tangent bundle $T(G/K)\cong G^\bbC/K^\bbC$ of rank-one Riemannian symmetric spaces $G/K$ of compact type, in terms of associated vector-functions.