Abstract
We prove that a normal vector field along a curve in \(\mathbb {R}^{3}\) is rotation minimizing (RM) if and only if it is parallel respect to the normal connection. This allows us to generalize all the results of RM vectors and frames to curves immersed in Riemannian manifolds.
Dedicated to Jaime Muñoz Masqué, with a deep gratitude for his generous assistance in the earlier years of my career, on the occasion of his 65th birthday
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Acknowledgments
The author wants to express his gratitude to his colleagues Marco Castrillón, Laureano González-Vega, Bert Jütler and Gema Quintana for the useful talks about the theory of RM vectors and frames.
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Etayo, F. (2016). Rotation Minimizing Vector Fields and Frames in Riemannian Manifolds. In: Castrillón López, M., Hernández Encinas, L., Martínez Gadea, P., Rosado María, M. (eds) Geometry, Algebra and Applications: From Mechanics to Cryptography. Springer Proceedings in Mathematics & Statistics, vol 161. Springer, Cham. https://doi.org/10.1007/978-3-319-32085-4_8
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DOI: https://doi.org/10.1007/978-3-319-32085-4_8
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