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- W2052570794 abstract "We consider the family of regular plane closed strictly convex curves and the family of differential equations of special type associated to positive-valued, periodic and continuous functions. Each curve and the solutions of a fixed differential equation determine a family of disjoint closed curves called φ -optics. In particular cases we obtain the family of α -isoptics and the family of arc-optic curves. The family of arc-optic curves is closely related to the solutions of the Ulam problem. We generalize the Bianchi–Auerbach equation derived for the problem of floating body to general case of φ -optics and we give some of its applications. We present the necessary and sufficient conditions for some geometric quantities connected in a natural way to φ -optics to be constant." @default.
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- W2052570794 date "2012-12-01" @default.
- W2052570794 modified "2023-09-29" @default.
- W2052570794 title "φ-optics and generalized Bianchi–Auerbach equation" @default.
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- W2052570794 doi "https://doi.org/10.1016/j.geomphys.2012.07.008" @default.
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