Geodesic
Tensor Product Surfaces in ℝ4and Lie Groups
Bulletin of the Malaysian Mathematical Society, Tome 33 (2010) no. 1 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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In this paper, we show that a hyperquadric M in ℝ 4 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 ℝ 4 with ℂ 2 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 ℝ 4 .
Classification : 53C40, 43A80, 30G35. 
@article{BMMS_2010_33_1_a4,
     author = {Siddika \"Ozkaldi and Yusuf Yayli},
     title = {Tensor {Product} {Surfaces} in {\ensuremath{\mathbb{R}}4and} {Lie} {Groups}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2010},
     volume = {33},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2010_33_1_a4/}
}
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Siddika Özkaldi; Yusuf Yayli. Tensor Product Surfaces in ℝ4and Lie Groups. Bulletin of the Malaysian Mathematical Society, Tome 33 (2010) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2010_33_1_a4/