Tensor product surfaces in R4 and lie groups

ÖZKALDI KARAKUŞ S., Yayuli Y.

Bulletin of the Malaysian Mathematical Sciences Society, cilt.33, sa.1, ss.69-77, 2010 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 1
  • Basım Tarihi: 2010
  • Dergi Adı: Bulletin of the Malaysian Mathematical Sciences Society
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.69-77
  • Anahtar Kelimeler: Bicomplex number, Euclidean curve, Lie group, Tensor product surfaces
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Hayır

Özet

In this paper, we show that a hyperquadric M in R4 is a Lie group by using bicomplex number product. By means of the tensor product surfaces of Euclidean planar curves, we determine some special subgroup of this Lie group M. Thus, we obtain Lie group structure of tensor product surfaces of Euclidean planar curves. Moreover, we obtain left invariant vector fields of these Lie groups. We identify R4 with C2 and consider the left invariant vector fields on these group which constitute complex structure. By means of these, we characterize these Lie groups as totally real, complex or slant in R4.