JP Journal of Geometry and Topology
Volume 2, Issue 3, Pages 245 - 257
(November 2002)
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A FINITELY HYPERBOLIC POINT IN A SMOOTH MANIFOLD
Howard Iseri (USA)
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Abstract:
One condition in Smarandache’s definition of a paradoxist geometry is the existence of a point and a line such that there are at least two lines through the point that are parallel to the given line, but not infinitely, many. We say that such a point is finitely hyperbolic relative to the line. This contrasts with there being exactly one parallel in Euclidean geometry and infinitely many in hyperbolic geometry. Surprisingly, the existence of a finitely hyperbolic point has been demonstrated for polyhedral surfaces with a reasonably defined geodesic. This result is extended here to smooth surfaces. |
| Keywords and phrases: Smarandache geometry, paradoxist geometry, finitely hyperbolic. |
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