Complex Osserman Kaehler Manifolds

TL;DR

This paper characterizes complex Osserman Kaehler manifolds, showing they have constant holomorphic sectional curvature in four dimensions and classifies higher-dimensional cases without three eigenvalues.

Contribution

It provides a complete characterization of complex Osserman Kaehler manifolds in four dimensions and classifies higher-dimensional cases lacking three eigenvalues.

Findings

H is complex Osserman iff it has constant holomorphic sectional curvature in 4D.

Classification of higher-dimensional complex Osserman Kaehler manifolds without 3 eigenvalues.

Establishes a link between the Osserman condition and constant holomorphic sectional curvature.

Abstract

Let H be a 4 dimensional almost Hermitian manifold which satisfies the Kaehler identity. Then H is complex Osserman if and only if H has constant holomorphic sectional curvature. We also classify in arbitrary dimensions all the complex Osserman Kaehler manifolds which do not have 3 eigenvalues.