Topology at infinity of complete gradient Schouten solitons

TL;DR

This paper investigates the geometric and topological properties at infinity of complete gradient Schouten solitons, revealing differences between shrinking and expanding cases regarding ends, potential functions, and volume growth.

Contribution

It provides new insights into the structure of Schouten solitons at infinity, including finiteness of ends for shrinking and connectedness for expanding solitons, without extra assumptions.

Findings

Shrinking Schouten solitons have finitely many ends.

Expanding Schouten solitons are connected at infinity.

Details on non-parabolicity and volume growth of ends.

Abstract

In this paper, we study ends of complete gradient non-trivial Schouten solitons. Without any additional assumptions, we show the shrinking ones have finitely many ends, and the expanding ones are connected at infinity. We also provide information regarding the non-parabolicity of the ends in the shrinking setting, and on the behavior of the potential function and volume growth in the expanding case.