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] 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.
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] 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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 15 Haziran 2007 |
| Yayımlandığı Sayı | Yıl 2007 Sayı: 013 |
- Makale Dosyaları