Bayrakdar, Tuna2024-06-122024-06-1220220219-88781793-6977https://doi.org/10.1142/S021988782350024Xhttps://hdl.handle.net/20.500.14551/20633In this work, we identify a smooth autonomous dynamical on a two-dimensional manifold with an exterior differential system (Sigma,I), where Sigma is a three-dimensional Riemannian manifold and I is the differential ideal generated by the contact forms on Sigma. We investigate the intrinsic and the extrinsic geometry of a surface in Sigma and show that for a particular dynamical system Sigma 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.en10.1142/S021988782350024Xinfo:eu-repo/semantics/closedAccessDynamical SystemsExterior Differential SystemsMinimal SurfacesTotally Geodesic SurfacesVector-FieldsTangentArticle1912Q2WOS:0008654593000162-s2.0-85140235726Q3