Minimal Surfaces in Three-Dimensional Riemannian Manifold Associated with a Second-Order ODE
Mediterranean Journal of Mathematics, cilt.15, sa.4, 2018 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 15 Sayı: 4
- Basım Tarihi: 2018
- Doi Numarası: 10.1007/s00009-018-1229-2
- Dergi Adı: Mediterranean Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Anahtar Kelimeler: jet bundle, Minimal surface, Riemannian geometry, second-order ODE, totally geodesic submanifold
- Trakya Üniversitesi Adresli: Hayır
Özet
We show that a surface corresponding to a first-order ODE is minimal in three-dimensional Riemannian manifold which is determined by the first prolongation of d y/ d x= p(x, y) if and only if pyy= 0. Accordingly, any linear first-order ODE describes a minimal surface which is not necessarily totally geodesic.