Castrillón López, MarcoRosado, M. EugeniaSoria, M. Eugenia2024-06-062024-06-062024-04-13López, M.C., Rosado, M.E. & Soria, A. Ruled Surfaces in 3-Dimensional Riemannian Manifolds. Mediterr. J. Math. 21, 97 (2024). https://doi.org/10.1007/s00009-024-02631-21660-54461660-545410.1007/s00009-024-02631-2https://hdl.handle.net/20.500.14352/104717In this work, ruled surfaces in 3-dimensional Riemannian manifolds are studied. We determine the expressions for the extrinsic and sectional curvatures of a parametrized ruled surface, where the former one is shown to be non-positive. We also quantify the set of ruling vector fields along a given base curve which allows us to define a relevant reference frame that we refer to as. The fundamental theorem of existence and equivalence of Sannia ruled surfaces in terms of a system of invariants is given. The second part of the article tackles the concept of the striction curve, which is proven to be the set of points where the so-called Jacobi evolution function vanishes on a ruled surface. This characterisation of striction curves provides independent proof for their existence and uniqueness in space forms and disproves their existence or uniqueness in some other casesengAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal articleopen accessRuled surfaceRiemannian mainfoldSannia frameJacobi fieldDifferential invariantStriction curveGeometría diferencial1204.04 Geometría Diferencial