Contributions to differential geometry of isotropic curves in the complex space

Yilmaz S.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.374, sa.2, ss.673-680, 2011 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 374 Sayı: 2
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.jmaa.2010.09.031
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.673-680
  • Anahtar Kelimeler: Classical differential geometry, E. Cartan frame, Isotropic curves, Isotropic cubic, Slant helix, SLANT HELIX, 3-SPACE
  • Dokuz Eylül Üniversitesi Adresli: Hayır

Özet

This work deals with classical differential geometry of isotropic curves in the complex space C(4). First, we study spherical isotropic curves and pseudo helices. Besides, in this section we introduce some special isotropic helices (type-1, type-2 and type-3 isotropic slant helices) and express some characterizations of them in terms of E. Cartan equations. Thereafter, we prove that position vector of an isotropic curve satisfies a vector differential equation of fourth order. Finally, we investigate position vector of an arbitrary curve with respect to E. Cartan frame by a system of complex differential equations whose solution gives components of the position vector. Solutions of the mentioned system and vector differential equation have not yet been found. Therefore, in terms of special cases, we present some special characterizations. (C) 2010 Elsevier Inc. All rights reserved.