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In this paper a family of curves—Riemannian cubics—in the unit sphere and the real projective plane is investigated. Riemannian cubics naturally arise as solutions to variational problems in Riemannian spaces. It is remarkable to find that an envelope of lines generated by a Riemannian cubic in one space is (nearly) a Riemannian cubic in another space.
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Krzysztof Krakowski (2005) studied this question.
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