On the Relation between Curvature, Diameter, and Volume of a Complete Riemannian Manifold

• Date: 2004
• Main Authors: Nguyen, Doan Tuan, Si, Duc Quang, Нгуєн, Доан Туан, Сі, Дук Куанг
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3867
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

In this note, we prove that if N is a compact totally geodesic submanifold of a complete Riemannian manifold M, g whose sectional curvature K satisfies the relation K ≥ k > 0, then \(d(m,N) \leqslant \frac{\pi }{{2\sqrt k }}\) for any point m ∈ M. In the case where dim M = 2, the Gaussian...