Rotational Symmetry of Conical K\"ahler-Ricci Solitons

TL;DR

This paper proves that certain expanding K"ahler-Ricci solitons with positive curvature and specific asymptotic behavior are uniquely rotationally symmetric, confirming a conjecture about their symmetry properties.

Contribution

The paper establishes the rotational symmetry of a class of expanding K"ahler-Ricci solitons under curvature and asymptotic conditions, confirming Cao's constructed examples.

Findings

Expanding K"ahler-Ricci solitons with positive holomorphic bisectional curvature are rotationally symmetric.

Such solitons asymptotic to K"ahler cones are uniquely characterized by Cao's examples.

The result confirms the conjecture that these solitons must be U(n)-rotationally symmetric.

Abstract

We show that expanding K\"ahler-Ricci solitons which have positive holomorphic bisectional curvature and are asymptotic to K\"ahler cones at infinity must be the U(n)-rotationally symmetric expanding solitons constructed by Cao.