| Autor: |
Paiva Barreto, Alexandre, Fontenele, Francisco |
| Předmět: |
|
| Zdroj: |
Revista Mathematica Iberoamericana; 2023, Vol. 39 Issue 4, p1437-1442, 6p |
| Abstrakt: |
In this paper, we prove that if Mn, n ≥ 3, is a complete Riemannian manifold with negative Ricci curvature and f: Mn →Rn+1 is an isometric immersion such that Rn+1\f(M) / is an open set that contains balls of arbitrarily large radius, then infM jAj D 0, where ∣A∣ is the norm of the second fundamental form of the immersion. In particular, an n-dimensional complete Riemannian manifold with negative Ricci curvature bounded away from zero cannot be properly isometrically immersed in a half-space of Rn+1 . This gives a partial answer to a question raised by Reilly and Yau. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
|
