Joachimsthal surfaces with nonzero constant Gaussian curvature
Algebraic, topological and analytical techniques in differential geometry and geom...
| Full text | |
| Author(s): |
Barreto, Alexandre Paiva
;
Fontenele, Francisco
;
Hartmann, Luiz
Total Authors: 3
|
| Document type: | Journal article |
| Source: | PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS; v. N/A, p. 8-pg., 2021-09-06. |
| Abstract | |
We prove that there are no regular algebraic hypersurfaces with non-zero constant mean curvature in the Euclidean space Rn+1, n >= 2, defined by polynomials of odd degree. Also we prove that the hyperspheres and the round cylinders are the only regular algebraic hypersurfaces with non-zero constant mean curvature in Rn+1, n >= 2, defined by polynomials of degree less than or equal to three. These results give partial answers to a question raised by Barbosa and do Carmo. (AU) | |
| FAPESP's process: | 18/23202-1 - Spectral invariants on pseudomanifolds |
| Grantee: | Luiz Roberto Hartmann Junior |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 18/03721-4 - Weingarten Surfaces, Self-Shrinkers and Hyperbolic Surfaces |
| Grantee: | Alexandre Paiva Barreto |
| Support Opportunities: | Regular Research Grants |
| 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 |