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ASYMPTOTIC CURVES ON SURFACES IN ℝ⁵

Departament de Geometria i Topologia, Facultat de Matemàtiques, Universitat de València, 46100-Burjassot, València, Spain

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M. A. S. RUAS

ICMC-USP, Dept. de Matemática, Av. do Trabalhador Sãocarlense, 400 Centro, Caixa Postal 668, CEP 13560-970, São Carlos (SP), Brazil

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, and

F. TARI

Department of Mathematical Sciences, University of Durham, Science Laboratories, South Rd, Durham DH1 3LE, United Kingdom

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https://doi.org/10.1142/S0219199708002806Cited by:7 (Source: Crossref)

Abstract

We study asymptotic curves on generically immersed surfaces in ℝ⁵. We characterize asymptotic directions via the contact of the surface with flat objects (k-planes, k = 1 - 4), give the equation of the asymptotic curves in terms of the coefficients of the second fundamental form and study their generic local configurations.

Keywords:

AMSC: 53A05, 58K05, 34A09, 37C10

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