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


BAYRAKDAR T., Ergin A.

Mediterranean Journal of Mathematics, vol.15, no.4, 2018 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 15 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.1007/s00009-018-1229-2
  • Journal Name: Mediterranean Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: jet bundle, Minimal surface, Riemannian geometry, second-order ODE, totally geodesic submanifold
  • Trakya University Affiliated: No

Abstract

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.