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

Bayrakdar, TUNA; ERGİN, ABDULLAH

doi:10.1007/s00009-018-1229-2

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

Bayrakdar T., ERGİN A. 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: Minimal surface, totally geodesic submanifold, second-order ODE, jet bundle, Riemannian geometry., CONSTANT MEAN-CURVATURE, EQUIVALENCE PROBLEM, CONNECTIONS, GEOMETRY, SYSTEMS, FORMULA
Akdeniz University Affiliated: Yes

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