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• W2912896414 abstract "Abstract We study frames in ℝ 3 and mapping from a surface M in ℝ 3 to the space of frames. We consider in detail mapping frames determined by a unit tangent principal or asymptotic direction field U and the normal field N . We obtain their generic local singularities as well as the generic singularities of the direction field itself. We show, for instance, that the cross-cap singularities of the principal frame map occur precisely at the intersection points of the parabolic and subparabilic curves of different colours. We study the images of the asymptotic and principal foliations on the unit sphere by their associated unit direction fields. We show that these curves are solutions of certain first order differential equations and point out a duality in the unit sphere between some of their configurations." @default.
• W2912896414 created "2019-02-21" @default.
• W2912896414 creator A5035645097 @default.
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• W2912896414 date "2019-01-26" @default.
• W2912896414 modified "2023-10-16" @default.
• W2912896414 title "Frame and direction mappings for surfaces in ℝ3" @default.
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• W2912896414 doi "https://doi.org/10.1017/prm.2018.42" @default.
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