Bertrand and Mannheim curves of framed curves in the 4-dimensional Euclidean space
نویسندگان
چکیده
A Bertrand curve in the 4-dimensional Euclidean space is a whose first normal line same as of another curve. On other hand, Mannheim second or third In this paper, we investigate not only and curves regular curves, but also singular curves. As consider framed We give conditions for to become It well-known that do exist under condition space. However, even
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ژورنال
عنوان ژورنال: Journal of Geometry
سال: 2023
ISSN: ['0047-2468', '1420-8997']
DOI: https://doi.org/10.1007/s00022-023-00673-7