In the present study we consider spherical product surfaces X = axb of two 2D curves in E3. We prove that if a spherical product surface patch X = axb has vanishing Gaussian curvature K (i.e. a flat surface) then either a or b is a straight line. Further, we prove that if a(u) is a straight line and b(v) is a 2D curve then the spherical product is a non-minimal and flat surface. We also prove that if b(v) is a straight line passing through origin and a(u) is any 2D curve (which is not a line) then the spherical product is both minimal and flat. We also give some examples of spherical product surface patches with potential applications to visual cyberworlds.
['Kadri Arslan', 'Betül Bulca', 'B. K. Bayram', 'Günay Öztürk', 'Hassan Ugail']
On Spherical Product Surfaces in E3