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Extrema of principal curvature and symmetry

Published online by Cambridge University Press:  20 January 2009

J. W. Bruce  and
F. Tari
J. W. Bruce
Affiliation:
Department of Pure Mathematics The University P.O. Box 147 Liverpool L69 3BX, U.K.
F. Tari
Affiliation:
Department of Pure Mathematics The University P.O. Box 147 Liverpool L69 3BX, U.K.
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Abstract

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In this paper we show that away from umbilic points certain measures of the local reflectional symmetry of a surface in Euclidean 3-space are detected by the extrema of the sectional curvatures along lines of curvature. There are two types of reflectional symmetry, with one detected by the contact between the surface and spheres, and in this case the result is due to Porteous and is 20 years old. We show that an analogous result remains true for the second type of symmetry.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 2 , June 1996 , pp. 397 - 402
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

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