Geometry of a surface in Riemannian 3-manifold corresponding to a smooth autonomous dynamical system

Abstract

In this work, we identify a smooth autonomous dynamical on a two-dimensional manifold with an exterior differential system [Formula: see text], where [Formula: see text] is a three-dimensional Riemannian manifold and [Formula: see text] is the differential ideal generated by the contact forms on [Formula: see text]. We investigate the intrinsic and the extrinsic geometry of a surface in [Formula: see text] and show that for a particular dynamical system [Formula: see text] admits a totally geodesic surface determined by a constant value of a coordinate function. We also exhibit that such a surface may define intrinsically nonflat minimal surface which is not necessarily totally geodesic.