Yıl 2019, Cilt 12 , Sayı 2, Sayfalar 182 - 187 2019-10-03

Shape Operator via Darboux Frame Curvatures and Its Applications

Bahar Uyar Düldül [1] , Mustfa Düldül [2]


We present the shape operator’s matrix of a surface along a surface curve. By using the obtained
matrix, we give a short proof of the Beltrami-Enneper theorem. Also, we give a new method for 
determining the well-known geodesic curves of a plane, a sphere and a circular cylinder by using 
the relation between the ordinary curvatures of the geodesic and the curvatures of the surface.

Shape operator, Darboux frame, curvature, geodesic curve
  • [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.
Birincil Dil en
Bölüm Araştırma Makalesi
Yazarlar

Yazar: Bahar Uyar Düldül

Yazar: Mustfa Düldül

Tarihler

Yayımlanma Tarihi : 3 Ekim 2019

Bibtex @araştırma makalesi { iejg628075, journal = {International Electronic Journal of Geometry}, issn = {}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2019}, volume = {12}, pages = {182 - 187}, doi = {}, title = {Shape Operator via Darboux Frame Curvatures and Its Applications}, key = {cite}, author = {Düldül, Bahar Uyar and Düldül, Mustfa} }
APA Düldül, B , Düldül, M . (2019). Shape Operator via Darboux Frame Curvatures and Its Applications. International Electronic Journal of Geometry , 12 (2) , 182-187 . Retrieved from https://dergipark.org.tr/tr/pub/iejg/issue/49199/628075
MLA Düldül, B , Düldül, M . "Shape Operator via Darboux Frame Curvatures and Its Applications". International Electronic Journal of Geometry 12 (2019 ): 182-187 <https://dergipark.org.tr/tr/pub/iejg/issue/49199/628075>
Chicago Düldül, B , Düldül, M . "Shape Operator via Darboux Frame Curvatures and Its Applications". International Electronic Journal of Geometry 12 (2019 ): 182-187
RIS TY - JOUR T1 - Shape Operator via Darboux Frame Curvatures and Its Applications AU - Bahar Uyar Düldül , Mustfa Düldül Y1 - 2019 PY - 2019 N1 - DO - T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 182 EP - 187 VL - 12 IS - 2 SN - -1307-5624 M3 - UR - Y2 - 2019 ER -
EndNote %0 International Electronic Journal of Geometry Shape Operator via Darboux Frame Curvatures and Its Applications %A Bahar Uyar Düldül , Mustfa Düldül %T Shape Operator via Darboux Frame Curvatures and Its Applications %D 2019 %J International Electronic Journal of Geometry %P -1307-5624 %V 12 %N 2 %R %U
ISNAD Düldül, Bahar Uyar , Düldül, Mustfa . "Shape Operator via Darboux Frame Curvatures and Its Applications". International Electronic Journal of Geometry 12 / 2 (Ekim 2019): 182-187 .
AMA Düldül B , Düldül M . Shape Operator via Darboux Frame Curvatures and Its Applications. International Electronic Journal of Geometry. 2019; 12(2): 182-187.
Vancouver Düldül B , Düldül M . Shape Operator via Darboux Frame Curvatures and Its Applications. International Electronic Journal of Geometry. 2019; 12(2): 187-182.