ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES
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
ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES
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,
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- [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.
- Başlangıç: 2020
- Yayıncı: Kütahya Dumlupınar Üniversitesi
Sayıdaki Diğer Makaleler
ON DIFFERENTIAL GEOMETRY OF THE LORENTZ SURFACES
TÜRKİYE MACROFUNGUSLARI İÇİN YENİ BİR CİNS: JAAPIA Bres.
MAKSiMUM YAGIŞLARIN BOLGESEL ZAMAN DAGILIMI iÇiN FONKSiYONEL YAKLAŞIMLAR
Ömer Levend Aşıkoğlu, Ertuğrul BENZEDEN
LYAPUNOV METODU iLE FARK DENKLEMLERiNiN KARARLILIGININ BELiRLENMESi
A.Burcu Özyurt Serim, Mustafa Bayram
AÇIK-OCAK iŞLETMELERiNDE HÜRİSTİK TABANLI KAMYON SEVK SiSTEMLERi
GAUSS AND CODAZZI-MAINARDI FORMULAE
PROPOSAL OF A SOLUTION TO FUZZY TRANSPORTATION PROBLEM USING FUZZY SET APPROACH
AMİNO ASİT SİSTEİNİN GEÇİŞ METAL KOMPLEKSLERİNİN SENTEZİ VE KARAKTERİZASYONU