Shape Operator via Darboux Frame Curvatures and Its Applications
INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, cilt.12, sa.2, ss.182-187, 2019 (ESCI, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 12 Sayı: 2
- Basım Tarihi: 2019
- Dergi Adı: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.182-187
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
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.