A Study On Quaternionic \(B_2\)-Slant Helix In Semi-Euclidean 4-Space

Faik Babadağ


In this work, we defined a quaternionic \(B_2\)-slant helix in semi-Euclidean space \(\mathbb{E}_2^4\). Then we gave Frenet formulae for the quaternionic curve in semi-Euclidean space \(\mathbb{E}_2^4\). Also, we investigated some necessary and sufficient conditions for a space curve to be a quaternionic \(B_2\)-slant helix according to quaternionic curves in semi-Euclidean space \(\mathbb{E}_2^4\).


\(B_2\)slant helices; Semi-Euclidean space; Helices; Semi-quaternions

Full Text:



A.C. Çöken and A. Tuna, On the quaternionic inclined curves in the semi-Euclidean space (E^4_2), Applied Mathematics and Computation 155 (2004), 373–389.

K. Bharathi and M. Nagaraj, Quaternion valued function of a real variable Serret-Frenet formulae, Indian J. Pure Appl. Math. 18 (6) (1987), 507–511.

B. Rosenfeld, Geometry of Lie Groups, Kluwer Academic Publishers, Netherlands (1997).

M. Özdemir and A.A. Ergin, Rotation with unit timelike quaternions in Minkowski 3-space, Journal of Geometry and Physics 56 (2006), 322–336.

S. Izumiya and N. Takeuchi, New special curves and developable surfaces, Turk J. Math. 28 (2004),


DOI: http://dx.doi.org/10.26713%2Fjims.v8i3.390

eISSN 0975-5748; pISSN 0974-875X