LINES OF PRINCIPAL CURVATURE FOR MAPPINGS WITH WHITNEY UMBRELLA SINGULARITIES
1986 年 38 巻 4 号 p. 551-559
詳細
1986 年 38 巻 4 号 p. 551-559
The pattern of lines of principal curvature near Whitney umbrella singularities of mappings of surfaces M into {R^3} are established. Sufficient conditions for the stability of the whole configuration of lines of principal curvature, under small perturbations of the mappings are given. These sufficient conditions are satisfied by a dense set in the space of {C^r}-mappings of M into {R^3}, r ≥ 4, endowed with the {C^2}-topology.
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