Shape Operator via Darboux Frame Curvatures and Its Applications

We present the shape operator’s matrix of a surface along a surface curve. By using the obtained

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  • [1] Gray, A., Abbena, E. and Salamon, S., Modern differential geometry of curves and surfaces with Mathematica, 3rd Edition, Chapman Hall CRC, 2006.
  • [2] O’Neill, B., Elementary Differential Geometry, Academic Press, 1966.
  • [3] Uyar Düldül, B. and Çalışkan, M., On the geodesic torsion of a tangential intersection curve of two surfaces in R3. Acta Math. Univ. Comenian. 82 (2013), 177-189.
  • [4] Ye, X. and Maekawa, T., Differential geometry of intersection curves of two surfaces. Comput. Aided Geom. Design 16 (1999), 767-788.