ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES

Nejat Ekmekci; Yılmaz Tuncer

EN TR

ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES

Abstract

In this paper we have defined the sign functions £1' £2' t3' £4' t5 and the vector fields Xu' Xv' nu and n , which have taken derivatives with (u,v) parameters of the tangent vector field X of any surface in Lorentz space and we get fundamental forms, Weingarten equations, Olin-Rodrigues and Gauss formulae. Beside these we calculate Gauss and mean curvatures.

Keywords

Lorenz Surface,Fundamental Forms,Curvatures,Weingarten Formulae

References

[1] B. O'Neill, Semi Riemannian Geometry With Applications To Relativity, Academic Press. Newyork, 1983.
[2] R.S. Millman, G.D. Parker, Elements of Differential Geometry, Prentice Hall, Englewood Cliffs, New Jersey, 1987.
[3] R.W. Sharpe, Differential Geometry, Graduate Text in Mathematics 166,Canada,1997.
[4] John M. Lee, Riemannian Manifolds, An 'Introduction To Curvature, Graduate Text in Mathematics 176, USA,1997.
[5] K. Nornizu and Kentaro Yano, On Circles and Spheres in Riemannian Geometry, Math.Ann. ,210, 1974.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Nejat Ekmekci ^* This is me

Yılmaz Tuncer This is me

Publication Date

June 15, 2007

Submission Date

March 16, 2007

Acceptance Date

May 15, 2007

Published in Issue

Year 2007 Number: 013

IZ

https://izlik.org/JA85NX22PM

Cite

RIS / Bibtex

APA

Ekmekci, N., & Tuncer, Y. (2007). ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES. Journal of Science and Technology of Dumlupınar University, 013, 20-24. https://izlik.org/JA85NX22PM

AMA

1.Ekmekci N, Tuncer Y. ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES. DPÜFBED. 2007;(013):20-24. https://izlik.org/JA85NX22PM

Chicago

Ekmekci, Nejat, and Yılmaz Tuncer. 2007. “ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES”. Journal of Science and Technology of Dumlupınar University, nos. 013: 20-24. https://izlik.org/JA85NX22PM.

EndNote

Ekmekci N, Tuncer Y (June 1, 2007) ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES. Journal of Science and Technology of Dumlupınar University 013 20–24.

IEEE

[1]N. Ekmekci and Y. Tuncer, “ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES”, DPÜFBED, no. 013, pp. 20–24, June 2007, [Online]. Available: https://izlik.org/JA85NX22PM

ISNAD

Ekmekci, Nejat - Tuncer, Yılmaz. “ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES”. Journal of Science and Technology of Dumlupınar University. 013 (June 1, 2007): 20-24. https://izlik.org/JA85NX22PM.

JAMA

1.Ekmekci N, Tuncer Y. ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES. DPÜFBED. 2007;:20–24.

MLA

Ekmekci, Nejat, and Yılmaz Tuncer. “ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES”. Journal of Science and Technology of Dumlupınar University, no. 013, June 2007, pp. 20-24, https://izlik.org/JA85NX22PM.

Vancouver

1.Nejat Ekmekci, Yılmaz Tuncer. ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES. DPÜFBED [Internet]. 2007 Jun. 1;(013):20-4. Available from: https://izlik.org/JA85NX22PM