Minimal Surfaces in Three-Dimensional Riemannian Manifold Associated with a Second-Order ODE

Bayrakdar T., ERGİN A. A.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.15, sa.4, 2018 (SCI-Expanded) identifier identifier

  • 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: Minimal surface, totally geodesic submanifold, second-order ODE, jet bundle, Riemannian geometry., CONSTANT MEAN-CURVATURE, EQUIVALENCE PROBLEM, CONNECTIONS, GEOMETRY, SYSTEMS, FORMULA
  • Akdeniz Üniversitesi Adresli: Evet

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 if and only if . Accordingly, any linear first-order ODE describes a minimal surface which is not necessarily totally geodesic.