Bicomplex number and tensor product surfaces in R⁴₂

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 totall...

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Збережено в:
Бібліографічні деталі
Дата:2012
Автори: Karakuş, S.Ö., Yayli, Y.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2012
Назва видання:Український математичний журнал
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Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/164151
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Опис
Резюме: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