An assortment of negatively curved ends

TL;DR

This paper constructs a broad class of closed manifolds whose products with the real line admit complete, negatively curved metrics with specific geometric properties near their ends, advancing understanding of negatively curved manifolds.

Contribution

It introduces a new class of closed manifolds with negatively curved product metrics, inspired by Ontaneda's work, detailing their geometric structure near the ends.

Findings

Existence of negatively curved metrics on manifold products

Exponential warping near one end of the manifold

Finite volume near the other end

Abstract

Motivated by a recent groundbreaking work of Ontaneda, we describe a sizable class of closed manifolds such that the product of each manifold in the class with the real line admits a complete metric of bounded negative sectional curvature which is an exponentially warped near one end and has finite volume near the other end.