Abstract
In our study, we establish k-type helices and (k,m)-type slant helices for equiform differential geometry of spacelike curves in 4-dimensional Minkowski space E₁⁴ and give some new characterizations for these helices. In this paper, we obtain characterizations equiform differential geometry of spacelike curves in 4-dimensional Minkowski space E$_{1}^{4}$. We establish $k$-type helices for this curves. Also we obtain $(k,m)$-type slant helices for equiform differential geometry of spacelike curves in Minkowski space-time.
Highlights
Helices, which are an important subject of the theory of curves in di¤erential geometry, are studied by physicists, engineers and biologists
Helix is described as an in 3-dimensional Euclidean space tangent vector ...eld forming a constant angle with a ...xed direction of the curve
Many authors were interested in helices to study it in Euclidean 3- and 4-space and they gave new characterizations for an helix
Summary
Helices, which are an important subject of the theory of curves in di¤erential geometry, are studied by physicists, engineers and biologists. Helix (or general helix) is described as an in 3-dimensional Euclidean space (or Minkowski) tangent vector ...eld forming a constant angle with a ...xed direction of the curve. Many authors were interested in helices to study it in Euclidean (or Minkowski) 3- and 4-space and they gave new characterizations for an helix. In the 4-dimensional Minkowski space k-type slant helices were de...ned in a study by Ali et al [1]: In addition, M.Y. Y¬lmaz and M.Bektas in [6] de...ned (k; m)-type slant helices in 4-dimensional Euclidean space. We establish k-type helices and (k; m)-type slant helices for equiform di¤erential geometry of spacelike curves in 4-dimensional Minkowski space E41 and give some new characterizations for these helices. C 2020 Ankara University C om munications Faculty of Sciences U niversity of A nkara-Series A 1 M athem atics and Statistics
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