Convex surfaces whose geodesics are planar |
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Authors: | Dr G R Burton |
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Institution: | (1) Mathematics Department, University College, Gower Street, WC1E 6BT London, England |
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Abstract: | It is shown that ifC is a convex surface, in euclidean space of dimension at least 3, having the property that all shortest paths onC between pairs of its points are planar, thenC is a sphere, a hyperplane or the boundary of an intersection of two half-spaces. No smoothness assumptions are made. |
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