Open Access
June 2012 Totally quasi-umbilic timelike surfaces in $\mathbb{R}^{1,2}$
Jeanne Clelland
Asian J. Math. 16(2): 189-208 (June 2012).


For a regular surface in Euclidean space $\mathbb{R}^3$, umbilic points are precisely the points where the Gauss and mean curvatures $K$ and $H$ satisfy $H^2 = K$; moreover, it is well-known that the only totally umbilic surfaces in $\mathbb{R}^3$ are planes and spheres. But for timelike surfaces in Minkowski space $\mathbb{R}^{1,2}$, it is possible to have $H^2 = K$ at a non-umbilic point; we call such points quasi-umbilic, and we give a complete classification of totally quasi-umbilic timelike surfaces in $\mathbb{R}^{1,2}$.


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Jeanne Clelland. "Totally quasi-umbilic timelike surfaces in $\mathbb{R}^{1,2}$." Asian J. Math. 16 (2) 189 - 208, June 2012.


Published: June 2012
First available in Project Euclid: 9 April 2012

zbMATH: 1245.53018
MathSciNet: MR2916361

Primary: 51B20 , 53C42
Secondary: 53A55 , 53C10

Keywords: method of moving frames , quasi-umbilic , Timelike surfaces

Rights: Copyright © 2012 International Press of Boston

Vol.16 • No. 2 • June 2012
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