RT Journal Article
T1 Ruled Surfaces in 3-Dimensional Riemannian Manifolds
A1 Castrillón López, Marco
A1 Rosado, M. Eugenia
A1 Soria, M. Eugenia
AB 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
PB SpringerLink
SN 1660-5446
SN 1660-5454
YR 2024
FD 2024-04-13
LK https://hdl.handle.net/20.500.14352/104717
UL https://hdl.handle.net/20.500.14352/104717
LA eng
NO López, 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/s00009-024-02631-2
DS Docta Complutense
RD 9 abr 2025