| Full text | |
| Author(s): |
Barreto, Alexandre Paiva
;
Fontenele, Francisco
Total Authors: 2
|
| Document type: | Journal article |
| Source: | REVISTA MATEMATICA IBEROAMERICANA; v. 39, n. 4, p. 6-pg., 2023-01-01. |
| Abstract | |
In this paper, we prove that if Mn, n > 3, is a complete Riemannian manifold with negative Ricci curvature and f : Mn symbolscript Rn+1 is an isometric immer-sion such that Rn+1\f (M) is an open set that contains balls of arbitrarily large radius, then infM IAI = 0, where IAI 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. (AU) | |
| FAPESP's process: | 19/20854-0 - Weingarten surfaces in R^3 and complete hypersurfaces with negative Ricci curvature in R^{n+1} |
| Grantee: | Alexandre Paiva Barreto |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - Brazil |
| FAPESP's process: | 18/03721-4 - Weingarten Surfaces, Self-Shrinkers and Hyperbolic Surfaces |
| Grantee: | Alexandre Paiva Barreto |
| Support Opportunities: | Regular Research Grants |