JP Journal of Geometry and Topology

The JP Journal of Geometry and Topology publishes articles in all branches of geometry and topology, with applications to physics. It covers areas such as differential geometry, algebraic topology, and geometric aspects of mathematical physics. Survey articles are also welcome.

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TUBE SURFACES IN A STRICT WALKER 3-MANIFOLD

Authors

  • Ameth Ndiaye
  • Mahamane Saminou Ali

Keywords:

canal surfaces, curves, mean curvature, Gauss curvature, Walker manifolds.

DOI:

https://doi.org/10.17654/0972415X24001

Abstract

In this paper, we investigate and present the geometric properties of tube surfaces in a strict Walker 3-manifold. By using the second fundamental form, the Gaussian and mean curvatures of tube surfaces are obtained. At the end, we give some examples to illustrate the main result.

Received: July 18, 2023
Accepted: September 15, 2023

References

S. Aslan and Y. Yayli, Canal surfaces with quaternions, Adv. Appl. Clifford Algebras 26 (2016), 31-38.

M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey, S. Nikevic and R. Vazquez-Lorenzo, The geometry of Walker manifolds, Synthesis Lectures on Mathematics and Statistics, Morgan and Claypool Publishers, Williston, VT, 2009.

M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1976, pp. 190-191.

B. Y. Chen, Geometry of submanifolds, Pure and Applied Mathematics, No. 22, Marcel Dekker, Inc., New York, 1973.

M. Gningue, A. Ndiaye and N. Renovat, Biharmonic curves in a strict Walker 3 manifold, Int. J. Math. Math. Sci. (2022), Art. ID 3855033, 6 pp.

Y. H. Kim, H. Liu and J. Qian, Some characterizations of canal surfaces, Bull. Korean Math. Soc. 53 (2016), 461-477.

D. W. Yoon, On the Gauss map of tubular surfaces in Galilean 3-space, Int. J. Math. Anal. 8(45) (2014), 2229-2238.

A. Ucum and K. Ilarslan, New types of canal surfaces in Minkowski 3-space, Adv. Appl. Clifford Algebras 26(1) (2016), 449-468.

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Published

2024-01-30

Issue

Vol. 30 No. 1 (2024)

Section

Articles

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How to Cite

TUBE SURFACES IN A STRICT WALKER 3-MANIFOLD. (2024). JP Journal of Geometry and Topology, 30(1), 1-16. https://doi.org/10.17654/0972415X24001

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