Proceedings of the American Mathematical Society

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A characterization of revolution quadrics by a system of partial differential equations

Author(s): Vladimir I. Oliker
Journal: Proc. Amer. Math. Soc. 138 (2010), 4075-4080.
MSC (2010): Primary 53A05, 53C40
Posted: June 29, 2010
MathSciNet review: 2679628
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Abstract | References | Similar articles | Additional information

Abstract: It is shown that existence of a global solution to a particular nonlinear system of second order partial differential equations on a complete connected Riemannian manifold has topological and geometric implications and that in the domain of positivity of such a solution, its reciprocal is the radial function of only one of the following rotationally symmetric hypersurfaces in ${\mathbb{R}}^{n+1}$ : paraboloid, ellipsoid, one sheet of a two-sheeted hyperboloid, and a hyperplane.

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