Extrema of principal curvature and symmetry

J.W. Bruce, F. Tari

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)397-402
JournalProceedings of the Edinburgh Mathematical Society (Series 2)
Volume39
Issue number2
DOIs
Publication statusPublished - 1996

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range (extremes)
curvature
symmetry

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Extrema of principal curvature and symmetry. / Bruce, J.W.; Tari, F.

In: Proceedings of the Edinburgh Mathematical Society (Series 2), Vol. 39, No. 2, 1996, p. 397-402.

Research output: Contribution to journalArticle

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AU - Tari, F.

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AB - 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.

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