Year: 2025
Type: article
Abstract: In this paper, we prove some generalizations of the Ambrose (or Myers) theorem for complete Riemannian manifolds. We observe that the problem of finding the Ricci curvature conditions that guarantee the compactness of the manifold is reduced to the problem of finding the proper oscillation conditions of second-order linear differential equations. The proof of the theorems is based on the Riccati comparison theorem and some related oscillation conditions.
Source: Journal of Science and Arts
Author: YASEMIN SOYLU
Institution: Giresun University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4415807820