Work

Hitchin's $α$-invariant and positive sectional curvature on homotopy $9$-spheres

Year: 2026

Type: preprint

Abstract: We prove that a smooth homotopy $9$-sphere admits a Riemannian metric of positive sectional curvature if and only if its Hitchin $α$-invariant vanishes, or equivalently if and only if it admits a Riemannian metric of positive scalar curvature.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.33474

Authors: He, Yang-Hui, Liu, Ziran, Yau, Shing-Tung

Institutions: Fudan University, Tsinghua University

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223918626

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Related to: 10