Browsing by Author "Ugail, Hassan"
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Item On spherical product surfaces in E3(IEEE, 2009) Bayram, Bengü; Öztürk, Günay; Ugail, Hassan; Earnshaw, R. A.; Qahwaji, R. S. R.; Willis, P. J.; Arslan, Kadri; Bulca, Betül; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0001-5861-0184; 0000-0002-1440-7050; AAG-8775-2021; AAG-7693-2021; 6603079141; 35226209600In the present study we consider spherical product surfaces X = alpha circle times beta of two 2D curves in E-3. We prove that if a spherical product surface patch X = alpha circle times beta has vanishing Gaussian curvature K (i.e. a flat surface) then either alpha or beta is a straight line. Further, we prove that if alpha(u) is a straight line and beta(v) is a 2D curve then the spherical product is a non-minimal and flat surface. We also prove that if beta(v) is a straight line passing through origin and alpha(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.