BERTRAND-B CURVES IN THE THREE DIMENSIONAL SPHERE

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Yerlikaya F., Aydemir İ.

FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, cilt.34, sa.2, ss.261-273, 2019 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 34 Sayı: 2
• Basım Tarihi: 2019
• Doi Numarası: 10.22190/fumi1902261y
• Dergi Adı: FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
• Sayfa Sayıları: ss.261-273
• Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

We define a Bertrand-B curve alpha in the three dimensional sphere S-3(r) such that there exists an isometry phi of S-3 (r), satisfying (phi omicron beta) (s) = X (s, t(s)) for another curve beta and both curves have common binormal geodesics at corresponding points. We analyze the condition of being Bertrand-B curves in S-3(r) and prove that the immersed curve with curvatures epsilon(1),epsilon(2) in S-3(r) is a Bertrand-B curve if and only if it satisfies epsilon(2)(1) + epsilon(2)(2) = 1. Also, we analyze some conclusions about a pair of Bertrand-B curves in S-3(r). As an application, we give an example that the conclusions are verified.