Abstract
In this paper, we investigate a general formulation for inextensible*ows of semi-real quaternionic curve in R2. We obtain necessary and su¢ cientconditions for inextensible *ow of semi-real quaternionic curves. Moreover, wegive the evolution equation of curvatures as a partial diğerential equation
Highlights
The Irish mathematician Hamilton wanted to generalize the complex numbers by introducing a three-dimensional object failed in the sense that the algebra he constructed for these three-dimensional object did not have the desired properties and he discovered the quaternion in 1843
We investigate a general formulation for inextensible ‡ows of semi-real quaternionic curve in R42
Quaternions can be represented as the sum of a scalar and a vector. They are applied to mechanic and physics
Summary
The Irish mathematician Hamilton wanted to generalize the complex numbers by introducing a three-dimensional object failed in the sense that the algebra he constructed for these three-dimensional object did not have the desired properties and he discovered the quaternion in 1843. They de...ned Serret-Frenet formulae for quaternionic curves in R4, by using the formulae in R3. After these studies, a lot of articles about quaternionic curves are published in R3 and R4. SerretFrenet formulas for quaternionic curves and quaternionic inclined curves have been de...ned in Semi-Euclidean space by Çöken and Tuna [2]. Curvature ‡ows, inextensible, semi real quaternionic curve, semiEuclidean space. Körp¬nar and Bas have investigated inextensible ‡ows of quaternionic curves in Euclidean space R4 [12]. Our aim is to study inextensible ‡ow of semi-real quaternionic curves in R42. We give necessary and su¢ cient conditions for inextensible ‡ows of semi-real quaternionic curves. We give the evolution equation of curvatures as a partial differential equation
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