# Gradient K\"ahler-Ricci solitons with nonnegative orthogonal bisectional curvature

## TL;DR

This paper proves that complete shrinking gradient K"ahler-Ricci solitons with positive orthogonal bisectional curvature are compact and provides a classification for those with nonnegative curvature.

## Contribution

It establishes a compactness result and classifies complete shrinking gradient K"ahler-Ricci solitons under orthogonal bisectional curvature conditions.

## Key findings

- Complete shrinking gradient K"ahler-Ricci solitons with positive orthogonal bisectional curvature are compact.
- A classification of such solitons with nonnegative orthogonal bisectional curvature is provided.

## Abstract

In this paper, we prove that any complete shrinking gradient K\"ahler-Ricci solitons with positive orthogonal bisectional curvature must be compact. We also obtain a classification of the complete shrinking gradient K\"ahler-Ricci solitons with nonnegative orthogonal bisectional curvature.