Stenzel's Ricci-flat Kaehler metrics are not projectively induced

TL;DR

This paper proves that the Ricci-flat Kähler metrics constructed by Stenzel on cotangent bundles cannot be holomorphically and isometrically immersed into complex projective space, highlighting limitations of such geometric embeddings.

Contribution

It demonstrates the non-existence of projective inducedness for Stenzel's Ricci-flat Kähler metrics on cotangent bundles of symmetric spaces.

Findings

Stenzel's metrics are not projectively induced

No holomorphic isometric immersion into complex projective space exists

Highlights limitations of embedding Ricci-flat Kähler metrics

Abstract

We investigate the existence of a holomorphic and isometric immersion in the complex projective space for the complete Ricci-flat Kaehler metrics constructed by M. B. Stenzel on the cotangent bundle of a compact, rank one, globally symmetric space.