GENERELIZED HELICES ON N-DIMENSIONAL RIEMANN-OTSUKI SPACES

Year 2019, Volume: 12 Issue: 1, 6 - 11, 05.08.2019

Jeta Alo

https://doi.org/10.20854/bujse.561471

Abstract

In
this paper the well-known properties of helices in Euclidian 3-space are
extended to n-dimensional Riemann-Otsuki space. We define the infinitesimal
deformations of curves in Riemann-Otsuki space and obtain the condition such
that the given deformation of a curve defines a generalized Helix in this space. 

Keywords

Riemann-Otsuki Spaces, Infinitesimal Deformations, Generelized Helices

References

• HAYDEN, H.A., 1931, Deformation of a curve in a Riemannian n-space which displace certain vectors parallelly at each point, Proc. London Math. Soc. (2), 32, 321-336.
• OTSUKI, T., 1958, Tangent Bundles of Order 2 and General Connections, Math. J.Okayama Univ., 8, 143-179.
• OTSUKI, T., 1960, On General Connections I, Math. J. Okayama Univ., 9, 99-164.
• OTSUKI, T., 1961, On General Connections II, Math. J. Okayama Univ., 10, 113-124
• Nadj, Dj.F.,1981, On Subspaces of Riemann-Otsuki Space, Publ. de l’Inst. MathBeograd, 30 (44), 53-58
• Nadj, Dj.F.,1981, On the Orthogonal Spaces of the Subspaces of a Riemann-OtsukiSpace , Zbornik Radova PMF Novi Sad, 11, 201-208
• MOOR, A., 1978, Otsukische Übertragung mit Rekurrentem Masstensor, Acta Sci.Math., 40, 129-142.
• MOOR, A., 1979, Über die Veranderung der Lange der Vektoren in Weyl-Otsukischen Raumen, Acta Sci. Math., 41, 173-185
• NADJ, Dj.F., 1986 The Frenet Formula of Riemann-Otsuki space, Zbornik RadovaPMF Novi Sad, 16, (1), 95-106.
• YANO, K., ADATI, T., 1944, Paralel tangent deformations, concircular transformation and concurrent vector field, Proc. Imp. Acad., 20, No3, 123-127
• YANO, K.,Kazuo, T., Yasuro, T.,1948, On infinitesimal deformations of curves inspaces with linear connection, Jap, J, Math., Volume 19, 433-477.