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Constant Rank Theorems under Intermediate Ricci Curvature

Year: 2026

Type: preprint

Abstract: We prove two constant rank theorems for the Ricci tensor in two geometric settings: manifolds with harmonic curvature and gradient Ricci solitons. In both cases, if the $k$-intermediate Ricci curvature satisfies $\Ric_k\geq0$ for some $1\leq k\leq n-2$, then the Ricci tensor has constant rank and its nullity distribution is parallel. In the complete case, the universal cover splits isometrically along the Ricci-null directions. We also show that the range $1\leq k\leq n-2$ is sharp: in every dimension $n\geq4$, nonnegative Ricci curvature alone does not imply the constant rank property in either setting.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.17691

Authors: Lai, Mijia, Wu, Guoqiang

Institutions: Zhejiang Sci-Tech University, Zhejiang University of Science and Technology, Shanghai Jiao Tong University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7221755325

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