Abstract
In this paper, we introduce special Smarandache curves and obtain Frenet apparatus of a Smarandache curve in three dimensional Lie groups with a bi-invariant metric. Moreover, we give some relations between a helix or a slant helix curve and its Smarandache curve in three dimensional Lie groups.
Highlights
In the classical di¤erential geometry, curves theory is a most important work area
We introduce special Smarandache curves and obtain Frenet apparatus of a Smarandache curve in three dimensional Lie groups with a bi-invariant metric
We give some relations between a helix or a slant helix curve and its Smarandache curve in three dimensional Lie Groups
Summary
In the classical di¤erential geometry, curves theory is a most important work area. Special curves and their characterizations have been studied for a long time and are still being studied. The degenerate semi-Riemannian geometry of Lie group has been studied by Çöken and Çiftçi [6] In this work, they obtained a naturally reductive homogeneous semi-Riemannian space using the Lie group. In [11], Okuyucu et al de...ned slant helices in a three dimensional Lie group G with a bi-invariant metric as a curve : I R !G whose normal vector ...eld makes a constant angle with a left invariant vector ...eld. They de...ned Bertrand curves in [12]. We introduce special Smarandache curves in three dimensional Lie groups with a bi-invariant metric and obtain Frenet apparatus of a Smarandache curve in three dimensional Lie groups
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