On the inner curvature of the second fundamental form of helicoidal surfaces |
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Authors: | Christos Baikoussis Themis Koufogiorgos |
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Institution: | (1) Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece |
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Abstract: | Let M be a helicoidal surface in E
3, free of points of vanishing Gaussian curvature. Let H be the mean curvature and K
II
the curvature of the second fundamental form. In this note it is shown that the helicoidal surfaces satisfying K
II
=H are locally characterized by constancy of the ratio of the principal curvatures. Moreover it is proved that these helicoidal
surfaces are determined by a first order differential equation.
Research supported by E.E.C. contract CHRX-CT92-0050. |
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Keywords: | Mathematics Subject Classification (1991)" target="_blank">Mathematics Subject Classification (1991) 53A05 |
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