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Lines of principal curvature near singular end points of surfaces in \(\mathbb R^3\). (English) Zbl 1143.53008
Izumiya, Shyuichi (ed.) et al., Singularity theory and its applications. Papers from the 12th MSJ International Research Institute of the Mathematical Society of Japan, Sapporo, Japan, September 16–25, 2003. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-32-7/hbk). Advanced Studies in Pure Mathematics 43, 437-462 (2006).
The nets of principal curvature lines on surfaces embedded in Euclidean 3 space near their endpoints, at which the surfaces tend to infinity, are studied. Patterns of the most common and stable behaviors at the ends are also classified in generic families of surfaces depending on one parameter.
For the entire collection see [Zbl 1110.32001].

MSC:
53A05 Surfaces in Euclidean and related spaces
34C23 Bifurcation theory for ordinary differential equations
58K25 Stability theory for manifolds
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