%0 Journal Article
%A Castrillón López, Marco
%A Rosado, M. Eugenia
%A Soria, M. Eugenia
%T Ruled Surfaces in 3-Dimensional Riemannian Manifolds
%D 2024
%@ 1660-5446
%@ 1660-5454
%U https://hdl.handle.net/20.500.14352/104717
%X In 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 cases
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