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- W1925079851 abstract "Celestials are surfaces that contain at least two real circles through a general point. We present a partial classification of celestials in the three-sphere up to Moebius equivalence. In particular, we consider translational celestials, which are the Clifford translation or Euclidean translation of a circle along a circle. For this purpose we introduce the invariant and we believe that this invariant is of general interest in classical geometries and in the theory of real embedded surfaces. We obtain several corollaries from our classification of translational celestials up to projective type. For example, a surface in the three-sphere that contains exactly two great circles and two little circles through a general point is a Clifford torus and thus the Clifford translation of a great circle along a great circle. Another corollary is that a surface of degree eight that contains a great circle and a little circle through a general point is the Clifford translation of a great circle along a little circle. This partially confirms a conjecture that celestials in the three-sphere are, up to Moebius equivalence, either translational or of degree four [Skopenkov-Krasauskas, 2015]. Moreover, we use the projective type to classify such celestials up to homeomorphism. We show that Euclidean translational celestials are not Moebius equivalent to Clifford translational celestials. The projective type of surfaces of degree eight that contain two little circles through a general point is left as an open problem." @default.
- W1925079851 created "2016-06-24" @default.
- W1925079851 creator A5041212379 @default.
- W1925079851 date "2013-06-08" @default.
- W1925079851 modified "2023-09-27" @default.
- W1925079851 title "Clifford and Euclidean translations of circles" @default.
- W1925079851 hasPublicationYear "2013" @default.
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