Spacelike intersection curve of three spacelike hypersurfaces in \(E_1^4\)

B. Uyar Duldul, M. Caliskan

Abstract


In this paper, we compute the Frenet vectors and the curvatures of the spacelike intersection curve of three spacelike hypersurfaces given by their parametric equations in four-dimensional Minkowski space \(E_1^4\).

Keywords


Intersection curve; hypersurface.

Full Text:

PDF

References


Alessio, O., Geometria diferencial de curvas de intersecao de duas superfıcies implıcitas, TEMA Tend. Mat. Apl. Comput. 7 (2) (2006), 169–178.

Alessio, O., Guadalupe, I. V., Determination of a transversal intersection curve of two spacelike surfaces in Lorentz–Minkowski 3-Space (L^3), Hadronic Journal 30 (3) (2007), 315–342.

Alessio, O., Differential geometry of intersection curves in (R^4) of three implicit surfaces, Comput. Aided Geom. Des. 26 (2009), 455–471.

Duldul, M., On the intersection curve of three parametric hypersurfaces, Comput. Aided Geom. Des. 27 (2010), 118–127.

Goldman, R., Curvature formulas for implicit curves and surfaces, Comput. Aided Geom. Des. 22 (2005), 632–658.

Hartmann, E., (G^2) interpolation and blending on surfaces, The Visual Computer 12 (1996), 181–192.

Turgut, A., Spacelike and timelike ruled surfaces on the Minkowski 3-space (R^3_1), Ph. D. thesis, Ankara University, 1995.

O’Neill, B., Semi Riemannian Geometry, Academic Press, New York–London, 1983.

Walrave, J., Curves and surfaces in Minkowski space, Ph. D. thesis, K. U. Leuven. Fac. Science, Leuven, 1995.

Williams, M. Z., Stein, F. M., A triple product of vectors in four-space, Math. Mag. 37 (4) (1964), 230–235.

Willmore, T. J., An Introduction to Differential Geometry, Clarendon Press, Oxford, 1959.

Ye, X., Maekawa T., Differential geometry of intersection curves of two surfaces, Comput. Aided Geom. Des. 16 (1999), 767–788.

Yilmaz, S., Turgut, M., On the differential geometry of the curves in Minkowski space-time I, Int. J. Contemp. Math. Sciences 3 (27) (2008), 1343–1349.




DOI: http://dx.doi.org/10.2478/v10062-012-0019-8
Date of publication: 2015-07-15 00:00:00
Date of submission: 2016-01-11 18:29:51


Statistics


Total abstract view - 877
Downloads (from 2020-06-17) - PDF - 587

Indicators



Refbacks

  • There are currently no refbacks.


Copyright (c) 2016 B. Uyar Duldul, M. Caliskan