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Osculating Spheres of a Semi Real Quaternionic Curve in E2

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Abstract (2. Language): 
In this study, we define the osculating spheres of a semi real quaternionic curve in semi-Euclidean spaces E1 and We give the equation of the osculating spheres with respect to Frenet frames {to,nv^.J and {To,NVNVN3J.
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REFERENCES

References: 

[1] W. K. Clifford. Preliminary sketch of biquaternions, Proceedings of the London Mathematical Society, 4, 361-395, 1873.
[2] A. C. Çöken and A. Tuna. On the quaternionic inclined curves in the semi-Euclidean space E', Appl. Math. Comput. 155, 373-389, 2004.
[3] F. Kahraman, İ. Gök, and H. H. Hacısalihoğlu. On the quaternionic £>2 slant helices in the semi- Euclidean space Applied Mathematics and Computation, 218,6391-6400,
[4] J. I? Ward. Quaternions and Cayley Numbers, Kluwer Academic Publishers, Boston/London, 1997.
[5] K. Bharathi and M. Nagaraj. Quaternion Valued Function of a Real Variable Serret-Frenet Formulae, İndian Journal of Pure and Applied Mathematics, 18(6), 507-511, 1987.
[ 6] A. Tuna. Serret Frenet formulae for Quaternionic Curves in semi-Euclidean Space, Mas¬ter Thesis, Süleyman Demirel University, Graduate School of Natural and Applied Science, Department of Mathematics, İsparta, Turkey, 2002.
[ 7] H. H. Hacısalihogğlu. Diferensiyel Geometri, Faculty of Sciences, University of Ankara
Press, 1993.
This completes proof.

References
2012.
[8]
A. Sabuncuogğlu. Diferensiyel Geometri, Nobel Press, 2010.
REFERENCES
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[ 9] D. J. Struik. Differential Geometry, second ed., Addison-Wesley, Reading, Massachusetts.
1961.
[ 10] D. Sağglam. On the Osculating Spheres of a Real Quaternionic Curve in the Euclidean Space E4, İnternational Journal of Mathematical Combinatorics, 3, 46-53, 2012.
[ 11 ] E. Soytürk, K. İlarslan, and D. Sağglam. Osculating spheres and osculating circles of a curve in semi-Reimannian space, Communications, Faculty of Science, University of Ankara Series A1, 54 (2) ,39-48, 2005.

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