You are here

Home » Content

BİR WEYL UZAYININ GÖZÖNÜNE ALINAN HİPER YÜZEYLERİNİN BAZI ÖZELLİKLERİ

SOME PROPERTIES CONCERNING THE HYPERSURFACES OF A WEYL SPACE

Journal Name:

  • Sigma Mühendislik ve Fen Bilimleri Dergisi

Publication Year:

  • 2005

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
Let Wn be a hypersurface of the Weyl spaceWn+1 . Let * ( 1, 2, ..., ) = i vi n be tangent vector fields belonging to Wn and n be the normalized normal vector field of Wn . Consider the ( 1) n + - net ** * 1 2 ( ) , , ..., , n vv vn . By using the prolonged covariant differentiation, we first obtain the set of formulas corresponding to the Frenet formulas for Wn associated with a curve C on Wn having the tangent vector field 1 v . We then, derive two invariants concerning the orthogonal ennuple 1 2 ( , , ..., ) n vv v , ( 1, 2, ..., ) = i vi n being differentiable vector fields on Wn .
Bookmark/Search this post with
Abstract (Original Language): 
Wn , Wn+1 Weyl uzayının bir hiperyüzeyi olsun. * ( 1, 2, ..., ) = i vi n , Wn ’e ait teğet vektör alanları ve n, Wn ’in normalize edilmiş normal vector alanı olsun. ** * 1 2 ( ) , , ..., , n vv vn ( 1) n + -li şebeke göz önüne alınsın. Genelleştirilmiş kovaryant türev kullanılarak, önce Wn hiperyüzeyinin bir C eğrisinin 1 v teğet vector alanına bağlı olarak Frenet formüllerine tekabül eden formüller elde edilmiştir. Sonra, Wn ’de tanımlı ( 1, 2, ..., ) = i vi n orthogonal şebekesi yardımıyla iki invariyant tanımlanmıştır
FULL TEXT (PDF): 
PDF icon arastrmx_845_23_pp_41-56.pdf
  • 4
41-56
  • Turkish

REFERENCES

References: 

[1] Norden, A. : Affinely Connected Spaces, GRMFL, Moscow, (1976).
[2] Norden, A. , Yafarov, S. : Theory of Non-geodesic Vector Fields in Two Dimensional
Affinely Connected Spaces, Izv. , Vuzov, Math. , No. 12, 29-34, (1974).
[3] Hlavaty, V. : Les Courbes de la Variete Wn
, Memor. Sci. Math. , Paris, (1934).
[4] Uysal, S. A. , Özdeğer, A. : On the Chyshev Nets in a Hypersurface of a Weyl Space,
Journal of Geometry, V.51, 171-177, (1994).
[5] Tsareva, B. , Zlatanov, G. : On the Geometry of the Nets in the n -Dimensional Space of
Weyl, Journal of Geometry, Vol. 38, 182-197, (1955).
[6] Kaul, R. N. : Formulae Corresponding to Frenet’s Formulae, Acad. Roy. Bélgique, 41,
1292-1304, (1955).
[7] Akgün, L. Z. : Frenet Formulas For Curves in a Generalized Weyl Space, Ganita, Vol.51,
No.2, 149-164, (2000).

Thank you for copying data from http://www.arastirmax.com