Extrema of principal curvature and symmetry

J.W. Bruce; F. Tari

doi:10.1017/S0013091500023129

Extrema of principal curvature and symmetry

J.W. Bruce, F. Tari

Research output: Contribution to journal › Article (journal) › peer-review

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 language	English
Pages (from-to)	397-402
Journal	Proceedings of the Edinburgh Mathematical Society (Series 2)
Volume	39
Issue number	2
DOIs	https://doi.org/10.1017/S0013091500023129
Publication status	Published - 1996

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title = "Extrema of principal curvature and symmetry",

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.",

author = "J.W. Bruce and F. Tari",

year = "1996",

doi = "10.1017/S0013091500023129",

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T1 - Extrema of principal curvature and symmetry

AU - Bruce, J.W.

AU - Tari, F.

PY - 1996

Y1 - 1996

N2 - 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.

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.

U2 - 10.1017/S0013091500023129

DO - 10.1017/S0013091500023129

M3 - Article (journal)

SN - 0013-0915

VL - 39

SP - 397

EP - 402

JO - Proceedings of the Edinburgh Mathematical Society (Series 2)

JF - Proceedings of the Edinburgh Mathematical Society (Series 2)

IS - 2

ER -

Extrema of principal curvature and symmetry

Abstract

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