Affine Dupin Surfaces

Niebergall, Ross; Ryan, Patrick

doi:10.1090/S0002-9947-96-01458-4

Affine Dupin Surfaces
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by Ross Niebergall and Patrick J. Ryan PDF

Trans. Amer. Math. Soc. 348 (1996), 1093-1115 Request permission

Abstract:

In this paper we study nondegenerate affine surfaces in $\mathbb {R} ^{3}$ whose affine principal curvatures are constant along their lines of curvature. We give a complete local classification of these surfaces assuming that the lines of curvature are planar, and there are no umbilics.

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