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A note on differential geometry of the curves in \(E^4\). (English) Zbl 1151.53307

Summary: In this note, we prove that every regular curve in four dimensional Euclidean space satisfies a vector differential equation of fifth order. Thereafter, in the same space, a relation among curvatures functions of inclined curves is obtained in terms of harmonic curvatures, which is related with Smarandache geometries [L. F. Mao, Int. J. Math. Comb. 1, No. 1, 45–58 (2007; Zbl 1136.51304)].

MSC:

53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
53A04 Curves in Euclidean and related spaces

Citations:

Zbl 1136.51304
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