Lancret-type theorems in equiaffine space

Lancret-type theorems in equiaffine space

In this study we first introduce the notion of general helix in an equiaffine 3-space by the property that a fixed direction, called axis always, lies in the rectifying plane. We prove a Lancret-type theorem for equiaffine general helices. Using a similar argument, we also define equiaffine slant he...

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Bibliographic Details
Published in:Journal of geometry Vol. 115; no. 2
Main Authors: Ogrenmis, Meltem, Ogrenmis, Alper Osman
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01-08-2024
Springer Nature B.V
Subjects:
Geometry
Helices
Mathematics
Mathematics and Statistics
Theorems
General helix
Slant helix
53A15
53A04
Equiaffine space
Lancret’s Theorem
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Summary:In this study we first introduce the notion of general helix in an equiaffine 3-space by the property that a fixed direction, called axis always, lies in the rectifying plane. We prove a Lancret-type theorem for equiaffine general helices. Using a similar argument, we also define equiaffine slant helices and classify them.
ISSN:0047-2468
1420-8997
DOI:10.1007/s00022-024-00724-7