ASYMPTOTIC CURVES ON SURFACES IN ℝ5-Reference-Cited by-同舟云学术

ASYMPTOTIC CURVES ON SURFACES IN ℝ5

Published:2008-06 Issue:03 Volume:10 Page:309-335
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

ROMERO-FUSTER M. C.¹,RUAS M. A. S.²,TARI F.³

Affiliation:

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

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

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

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199708002806

Reference38 articles.

1. Monographs in Mathematics;Arnol'd V. I.,1985

2. Research Notes in Mathematics;Banchoff T.,1982

3. A note on First order Differential Equations of Degree Greater than One and Wavefront Evolution

4. Generic Geometry, Transversality and Projections

5. J. W. Bruce, P. J. Giblin and F. Tari, Real and Complex Singularities, Pitman Research Notes in Mathematics 333, ed. W. L. Marar (Longman, 1995) pp. 148–178.

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