RULED SURFACES WITH CONSTANT CURVATURES IN A STRICT WALKER 3-MANIFOLD

Papa Aly Cisse, Mamadou Eramane Bodian, Ameth Ndiaye

DOI Number
https://doi.org/10.22190/FUMI241218034C
First page
455
Last page
469

Abstract


In this paper, we give explicit descriptions for a family of ruled surfaces in a strict Walker 3-manifold with constant Gaussian or mean curvature according to the causal character of the surfaces (timelike, spacelike, and lightlike). For each causal character of the considered family of ruled surface, we start with the constant Gaussian curvature case and we end with the constant mean curvature situation.

Keywords

ruled surfaces, Walker 3-manifolds.

Full Text:

PDF

References


M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey, S. Nikčević and R. VazquezLorenzo: The Geometry of Walker Manifolds. G. Krantz (Ed.), Synthesis Lectures on Mathematics and Statistics, Washington University, St. Louis, 5. Morgan and Claypool Publishers, Williston, VT (2009).

G. Calvaruso and J. Van der Veken: Parallel surfaces in Lorentzian threemanifolds admitting a parallel null vector field. J. Phys. A: Math. Theor. 43 (2010), 325–207.

M. Chaichi, E. Garcia-Rio and M. E. Vazquez-Abal: Three-dimensional Lorentz manifolds admitting a parallel null vector field. J. Phys. A: Math. Gen. 38 (2005), 841–850.

A. S. Diallo, A. Ndiaye and A. Niang: Minimal graphs on three-dimensional Walker manifolds. Proceedings of the First NLAGA-BIRS Symposium, Dakar, Senegal, 425–438, Trends Math. Birkhauser/Springer, Cham (2020).

M. P. Do Carmo: Differential geometry of curves and surfaces. Prentice-Hall, Inc. Englewood Cliffs, NJ (1976).

M. A. Drame, A. Ndiaye and A. S. Diallo: 2-ruled hypersurfaces in a Walker 4-manifold. Facta Univ. Ser. Math. Inform. 39(1) (2024), 67–86.

K. L. Duggal and A. Benjacu: Lightlike Submanifolds of Semi-Riemannian Manifolds and Application; Mathematics and Its Applications. Kluwer Academic Publishers Group: Dordrecht, The Netherlands, (1996).

M. Emme: Imagine math. Milano: Springer (2012).

A. Niang: Surfaces minimales regees dans l’espace de Minkowski ou Euclidien oriente de dimension 3. Afrika Mat. 15(3) (2003), 117–127.

A. Niang, A. Ndiaye and A. S. Diallo: A Classification of Strict Walker 3-Manifold. Konuralp J. Math. 9(1) (2021), 148–153.

A. Niang, A. Ndiaye and A. S. Diallo: Minimals translation surfaces in a strict Walker 3-manifold. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 73(2) (2024), 554–568.

K. Nomizu and T. Sasaki: Affine Differential Geometry. Geometry of Affine Immersions. Cambridge Tracts in Mathematics Vol. 111, Cambridge University Press, Cambridge (1994).

I. Van de Woerstyne: Minimal surfaces of the 3-dimensional Minkowski space. Geometry and topology of submanifolds, II, Avignon (1988), 344–369.




DOI: https://doi.org/10.22190/FUMI241218034C

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)