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Helix preserving mappings
Author(s) -
Altunkaya Bülent,
Kula Levent
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6056
Subject(s) - mathematics , euclidean space , helix (gastropod) , euclidean geometry , pure mathematics , space (punctuation) , tangent space , type (biology) , tangent , mathematical analysis , geometry , computer science , ecology , snail , biology , operating system
In this study, we define two types of mappings that preserve the constant angle between the tangent vector field and the axis of a given helix in Euclidean spaces. The first type generates helices in the n‐dimensional Euclidean space from helices in the same space. The second type generates helices in the (n+1)‐dimensional Euclidean space from helices in the n‐dimensional Euclidean space. In addition, we give invariants of these mappings and study polynomial, rational, conical, ellipsoidal, and hyperboloidal helices supported by examples.