Tohoku Mathematical Journal
2007
June
SECOND SERIES VOL. 59, NO. 2

Tohoku Math. J.
59 (2007), 233-258

Title ON PAIRS OF GEOMETRIC FOLIATIONS ON A CROSS-CAP

Author Farid Tari

(Received December 9, 2005, revised November 10, 2006)
Abstract. We obtain the topological configurations of the lines of curvature, the asymptotic and characteristic curves on a cross-cap, in the domain of a parametrisation of this surface as well as on the surface itself.

2000 Mathematics Subject Classification. Primary 53A05; Secondary 58K05, 34A09.
Key words and phrases. Cross-caps, lines of principal curvature, asymptotic curves, characteristic curves, singularities.

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