Kahler manifolds with some Killing tensors

TL;DR

This paper classifies certain compact Kähler manifolds that admit specific J-invariant Killing tensors with particular eigenvalue structures, advancing understanding of their geometric properties.

Contribution

It provides a classification of compact, simply connected Kähler manifolds admitting J-invariant Killing tensors with specified eigenvalue multiplicities and constant eigenvalues.

Findings

Classification of manifolds with specified Killing tensor structures

Identification of eigenvalue multiplicity conditions

Insights into the geometric structure of such Kähler manifolds

Abstract

The aim of this paper is to classify compact, simply connected K\"ahler manifolds which admit J-invariant Killing tensor with two eigenvalues of multiplicity 2 and n-2 and with constant eigenvalue corresponding to 2-dimensional eigendistribution.