## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### An explicit characterization of spherical curves according to bishop frame and an approximately solution

**ABSTRACT**

In this paper, spherical curves are studied by using Bishop Frame. First, the differential equation characterizing the spherical curves is given. Then, we exhibit that the position vector of a curve which is lying on a sphere satisfies a third-order linear differential equation. Then we solve this linear differential equation by using Bernstein Series Solution Method.

**KEYWORDS**

PAPER SUBMITTED: 2018-11-01

PAPER REVISED: 2018-12-28

PAPER ACCEPTED: 2019-01-10

PUBLISHED ONLINE: 2019-03-09

- Wong , Y. C., On an Explicit Characterization of Spherical Curves, Proc. Am. Math. Soc., 34 (1972), 1, pp. 239-242
- Breuer ,S., Gottlieb, D., Explicit Characterization of Spherical Curves, Proc. Am. Math. Soc., 27 (1971), pp. 126-127
- Wong, Y. C., A global formulation of the condition for a curve to lie in a sphere, Monatsh. Math., 67 (1963), 363-365
- Mehlum, E., Wimp ,J., Spherical Curves and Quadratic Relationships for Special Functions, Austral. Mat. Soc., 27 ( 1985) pp. 111-124
- Kose ,O.,An Expilicit Characterization of Dual Spherical Curves, Doğa Mat. 12 (1998 ), 3, pp. 105-113
- Abdel Bakey , R. A.,An Explicit Characterization of Dual Spherical Curve, Commun. Fac. Sci. Univ. Ank. Series, 51 (2002), 2, pp. 1-9
- Ilarslan , K., et all., On the explicit characterization of spherical curves in 3-dimensional Lorentzian space, Journal of Inverse and Ill-posed Problems, 11 (2003), 4, pp. 389-397
- Kocayigit, H., et all., On the explicit characterization of spherical curves in n-dimensional Euclidean space, Journal of Inverse and Ill-posed Problems, 11 (2003), 3, pp. 245-254
- Ayyilidiz, N. , et all., A Characterization of Dual Lorentzian Spherical Curves in the Dual Lorentzian Space, Taiwanese Journal of Mathematics, 11 (2007), 4, pp. 999-1018
- Camci, C., et all., On the characterization of spherical curves in 3-dimensional Sasakian spaces, J. Math. Anal. Appl., 342 (2008),pp. 1151-1159
- Bishop, L. R., There is More Than one Way to Frame a Curve, Amer. Math. Monthly, 82 (1975), 3, pp. 246-251
- Bhatti, ,M.I., Brocken, B., Solutions of Differential Equations in a Bernstein Polynomial Basis, Bhatti Journal of Computational And Applied Mathematics. 205 (2007), pp. 272-280
- Işik ,O.R., et all., A rational approximation based on Bernstein polynomials for high order initial and boundary values problems, Applied Mathematics and Computation, 217 (2011), pp. 9438-945