A CHARACTERIZATION OF THE CATENOID AND HELICOID
2013 ◽
Vol 24
(06)
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pp. 1350045
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Keyword(s):
In this paper we show that a connected non-planar minimal surface whose asymptotic lines have the same geodesic curvature up to sign is a catenoid. As an application of this result we show that a connected non-planar minimal surface whose lines of curvature have the same geodesic curvature up to sign is a helicoid. Moreover, we show that the coordinates curves of the associate minimal surfaces to catenoid have the same geodesic curvature up to sign.
Keyword(s):
1994 ◽
Vol 209
(1)
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1983 ◽
Vol 6
(2)
◽
pp. 341-361
2019 ◽
Vol 2019
(753)
◽
pp. 159-191
◽
2009 ◽
Vol 194
◽
pp. 149-167
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1951 ◽
Vol 2
(1)
◽
pp. 47-47
Keyword(s):