TY  - JOUR
T1  - ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES
TT  - ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES
AU  - Ekmekci, Nejat
AU  - Tuncer, Yılmaz
PY  - 2007
DA  - June
JF  - Journal of Science and Technology of Dumlupınar University
JO  - DPÜFBED
PB  - Kütahya Dumlupınar Üniversitesi
WT  - DergiPark
SN  - 2651-2769
SP  - 20
EP  - 24
IS  - 013
LA  - en
AB  - 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.
KW  - Lorenz Surface
KW  - Fundamental Forms
KW  - Curvatures
KW  - Weingarten Formulae
N2  - 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.
CR  - [1] B. O'Neill, Semi Riemannian Geometry With Applications To Relativity, Academic Press. Newyork, 1983.
CR  - [2] R.S. Millman, G.D. Parker, Elements of Differential Geometry, Prentice Hall, Englewood Cliffs, New Jersey, 1987.
CR  - [3] R.W. Sharpe, Differential Geometry, Graduate Text in Mathematics 166,Canada,1997.
CR  - [4] John M. Lee, Riemannian Manifolds, An 'Introduction To Curvature, Graduate Text in Mathematics 176, USA,1997.
CR  - [5] K. Nornizu and Kentaro Yano, On Circles and Spheres in Riemannian Geometry, Math.Ann. ,210, 1974.
UR  - https://dergipark.org.tr/tr/pub/dpufbed/article/408031
L1  - https://dergipark.org.tr/tr/download/article-file/444382
ER  -