Bicomplex number and tensor product surfaces in R⁴₂

• Date: 2012
• Main Authors: Karakuş, S.Ö., Yayli, Y.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2012
• Series: Український математичний журнал
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/164151
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Bicomplex number and tensor product surfaces in R⁴₂/ S.Ö. Karakuş, Y. Yayli // Український математичний журнал. — 2012. — Т. 64, № 3. — С. 307-317. — Бібліогр.: 13 назв. — англ.

We show that a hyperquadric M in R⁴₂ is a Lie group by using the bicomplex number product. For our purpose, we change the definition of tensor product. We define a new tensor product by considering the tensor product surface in the hyperquadric M. By using this new tensor product, we classify totally real tensor product surfaces and complex tensor product surfaces of a Lorentzian plane curve and a Euclidean plane curve. By means of the tensor product surfaces of a Lorentzian plane curve and a Euclidean plane curve, we determine a special subgroup of the Lie group M. Thus, we obtain the Lie group structure of tensor product surfaces of a Lorentzian plane curve and a Euclidean plane curve. Moreover, we obtain left invariant vector fields of these Lie groups. We consider the left invariant vector fields on these groups, which constitute a pseudo-Hermitian structure. By using this, we characterize these Lie groups as totally real or slant in R⁴₂