Volume 33 • Number 1 • 2010   • Tensor Product Surfaces in ℝ4 and Lie Groups Siddika Özkaldi and Yusuf Yayli Abstract. 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. 2000 Mathematics Subject Classification: 53C40, 43A80, 30G35. Full text: PDF