Projectively induced rotation invariant K\"ahler metrics

TL;DR

This paper classifies certain Kähler-Einstein manifolds that can be embedded into complex projective space with rotation-invariant metrics, focusing on those with codimension up to 3.

Contribution

It provides a classification of rotation-invariant Kähler-Einstein manifolds admitting Kähler immersions into projective space with limited codimension.

Findings

Classification of such manifolds achieved

Identifies conditions for Kähler immersions

Highlights the role of rotation invariance in embeddings

Abstract

We classify K\"ahler-Einstein manifolds which admit a K\"ahler immersion into a finite dimensional complex projective space endowed with the Fubini-Study metric, whose codimention is not greater than 3 and whose metric is rotation invariant.