Sur les metriques admettant les plans comme surfaces minimales
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- by M. Bekkar PDF
- Proc. Amer. Math. Soc. 124 (1996), 3077-3083 Request permission
Abstract:
We establish the system of partial differential equations satisfied by the riemannian metrics on open subsets of ${\mathbb {R}}^{3}$ which admit planes as minimal surfaces. This is a nonlinear system of 10 partial differential equations, with the euclidian metric as a particular solution. In a previous work, we solved this system for axially symmetrical metrics. In this paper we linearize the system at the euclidian metric and solve the linear system. We obtain a 20-dimensional space of solutions.References
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Additional Information
- M. Bekkar
- Affiliation: Université de Haute Alsace, 4 rue des Frères Lumière, F 68093 Mulhouse cedex, France et Université d’Oran Es-Sénia, Institut de Mathématiques, Oran, Algérie
- Email: M.Bekkar{@}univ-mulhouse.fr
- Received by editor(s): March 15, 1995
- Communicated by: Christopher Croke
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3077-3083
- MSC (1991): Primary 49Q05, 53A10
- DOI: https://doi.org/10.1090/S0002-9939-96-03530-7
- MathSciNet review: 1346962