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math.DG2024
Curves and surfaces making a constant angle with a parallel transported direction in Riemannian spaces
Luiz C. B. da Silva, Gilson S. Ferreira, José D. da Silva
In the last two decades, much effort has been dedicated to studying curves and surfaces according to their angle with a given direction. However, most findings were obtained using…
math.DG2019
Curves orthogonal to a vector field in Euclidean spaces
Luiz C. B. da Silva, Gilson S. Ferreira
A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any…