Bicomplex number and tensor product surfaces in $ \mathbb{R}_2^4 $
| Autor: | S. Ö. Karakuş, Y. Yayli |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Ukrainian Mathematical Journal. 64:344-355 |
| ISSN: | 1573-9376 0041-5995 |
| DOI: | 10.1007/s11253-012-0651-z |
| Popis: | We show that a hyperquadric M in $ \mathbb{R}_2^4 $ 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 $ \mathbb{R}_2^4 $ . |
| Databáze: | OpenAIRE |
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