WHAT IS THE LOCUS OF THE CENTERS OF MEUSNIER SPHERES IN MINKOWSKI 3-SPACE?

Beyhan Yılmaz, Zehra Özdemir, Ismail Gök, Yusuf Yayli

DOI Number
-
First page
717
Last page
740

Abstract


In view of these basic facts, it is natural to ask the following geometric question:

" What is the locus of the centers of Meusnier spheres in 3-dimensional Minkowski space? "

In this study, we investigate the answer of the above question.


Keywords


Osculating sphere, Meusnier sphere, Evolute curve, Minkowski Space

Full Text:

PDF

References


Ali TA, Lopez R (2011) Slant helices in Minkowski space . J Korean Math Soc. doi: 10.4134/JKMS.2011.48.1.159.

Bukcu B, Karacan MK (2007) On the Involute and Evolute Curves of the Spacelike Curve with a Spacelike Binormal in Minkowski Space. Int J Contemp Math. Sciences 2:221-232

Iyigün E, Özdamar E (1994) On the Meusnier's theorem for Lorentzian Surfaces. Commun Fac Sci Univ Ank Series doi: 10.1501/Commua1_0000000468

Kızıltuğ S, Yaylı Y (2012) Timelike Curves on Timelike Parallel Surfaces in Minkowski space Math Aeterna, 2:689-700

Lopez R (2008) Differential Geometry of curves and surfaces in Lorentz-Minkowski space. arXiv:0810.3351v1[math.DG]

Soytürk E, İlarslan K, Sağlam D (2005) Osculating Spheres and Osculating Circles of a Curve in Semi-Riemannian Space. Commun Fac Sci Univ Ank Series doi: 10.1501/Commua1_0000000330

Uribe VR (2005) On Vertices focal curvatures and differential geometry of space curves. Bull Braz Math Soc. doi: 10.1007/s00574-005-0040-4

Uzunoğlu B, Gök İ, Yaylı Y (2013) Locus of the centers of Meusnier spheres in Euclidean 3-space. arXiv:1307.4213v1 [math.DG]


Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)