# Remarks on shrinking gradient K\"ahler-Ricci solitons with positive bisectional curvature

## TL;DR

This paper offers an alternative proof that shrinking gradient K"ahler-Ricci solitons with positive bisectional curvature are necessarily compact, building on previous results and methods by Munteanu, Wang, and Lei Ni.

## Contribution

It provides a new proof technique for a known classification result of shrinking gradient K"ahler-Ricci solitons with positive bisectional curvature.

## Key findings

- Shrinking gradient K"ahler-Ricci solitons with positive bisectional curvature are compact.
- The proof uses an argument by Munteanu and Wang as an alternative approach.
- The result confirms the classification of such solitons as compact manifolds.

## Abstract

In this short note, using an argument by Munteanu and Wang, we provide an alternative proof of the fact first obtained by Lei Ni that shrinking gradient K\"ahler-Ricci solitons with positive bisectional curvature must be compact.