A short proof of the generalized Bonnet theorem

Kanbay F.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.37, sa.10, ss.1488-1490, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 10
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1002/mma.2909
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1488-1490
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In three-dimensional Euclidean space E3, the Bonnet theorem says that a curve on a ruled surface in three-dimensional Euclidean space, having two of the following properties, has also a third one, namely, it can be a geodesic, that it can be the striction line, and that it cuts the generators under constant angle. In this work, in n dimensional Euclidean space En, a short proof of the theorem generalized for (k+1) dimensional ruled surfaces by Hagen in is given. Copyright (c) 2013 John Wiley & Sons, Ltd.