ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES

Öz

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.

Anahtar Kelimeler

• Lorenz Surface,Fundamental Forms,Curvatures,Weingarten Formulae

Kaynakça

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