Spherical Bertrand and PH-curves

Gümüş M.

19th International Geometry Symposium, Edirne, Turkey, 27 - 30 June 2022, vol.1, no.1, pp.155, (Summary Text)

  • Publication Type: Conference Paper / Summary Text
  • Volume: 1
  • City: Edirne
  • Country: Turkey
  • Page Numbers: pp.155
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

The theory of curves is one of the most important studies in differantial

geometry. Especialy Bertrand curves are highly common. The

linearity of the principal normal vector fields of any two curves is an

interesting problem and this problem was solved by Bertrand in 1850

[1]. Many papers on Bertrand curves have been puplished up to now.

In 1990 PH-curves were defined by Farouki and Sakkalis [2] . Izumiya

and Takeuchi showed in [3] a method how to get Bertrand curves from

an arbitrary spherical curve. In this study we state the latest studies

on Bertrand and PH-curves for example [4], [5]. Also we give some

results on Bertrand PH-curves in Euclidean and Minkowski spaces.