Parameterisation of developable surfaces by asymptotic lines
1996 ◽
Vol 54
(3)
◽
pp. 411-421
◽
Keyword(s):
An example of a “non-developable” surface of vanishing Gaussian curvature from W. Klingenberg's textbook is considered and its place in the theory of 2-dimensional developable surfaces is pointed out. The surface is found in explicit form. Other examples of smooth developable surfaces not allowing smooth asymptotic parametrisation are analysed. In particular, Hartman and Nirenberg's example (1959) is incorrect.
Keyword(s):
1863 ◽
Vol 12
◽
pp. 279-280
◽
Keyword(s):
1998 ◽
Vol 42
(03)
◽
pp. 207-215
◽
2010 ◽
Vol 467
(2128)
◽
pp. 1121-1140
◽
Keyword(s):