On the spherical indicatrices of curves in Galilean 4-space. (English) Zbl 1454.53014
Summary: Euclidean and non-Euclidean geometries can be considered as spaces that are invariant under a given group of transformations [F. Klein, Math. Ann. 43, 63–100 (1893; JFM 25.0871.01)]. The geometry established by this approach is called Cayley-Klein geometry. Galilean 4-space is simply defined as a Cayley-Klein geometry of the product space \(\mathbb{R}\times\mathbb{E}^3\) whose symmetry group is Galilean transformation group which has an important place in classical and modern physics.
MSC:
| 53A35 | Non-Euclidean differential geometry |
| 53A40 | Other special differential geometries |
| 53B25 | Local submanifolds |
Keywords:
Galilean 4D space; spherical indicatrices; \(ccr\)-curve; involute-evolute curves; Bertrand curve; helix; spherical curveCitations:
JFM 25.0871.01References:
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