ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES

Year 2007, Issue: 013, 20 - 24, 15.06.2007

Nejat Ekmekci Yılmaz Tuncer

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.