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Paper   IPM / M / 16949
School of Mathematics
  Title:   Asymptotic and binormal directions on surfaces sitting in the four-dimensional Euclidean space
  Author(s):  Mahdi khajeh Salehani
  Status:   To Appear
  Journal: Bull. Iranian Math. Soc.
  Supported by:  IPM
  Abstract:
This work was intended as an attempt at exploring, in a novel and systematic way, the geometric aspects of some local invariants and the analytic features of asymptotic and binormal directions on the surfaces immersed in the four-dimensional Euclidean space by looking more closely at the normal connection and extrinsic geometry of the surfaces, and also investigating the curvature ellipse, of a given surface, and its director circle. In fact, our local constructions lead to some global results on the existence of singularities of the surfaces.

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