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Projections from surfaces of revolution in the Euclidean plane

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Abstract

In this paper, we determine the class of surfaces of revolution S for which there exists a smooth map \(\Phi \) from a neighbourhood U of S to the Euclidean plane \(E^{2}\) preserving distances infinitesimally along the meridians and the parallels of S and sending the meridional arcs of \(U\cap S\) to straight lines of \(E^{2}\).

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References

  • Charitos, C., Papadoperakis, I.: On the existence of a perfect map from the 2-sphere to the Euclidean plane, Eighteen Essays in Non-Euclidean Geometry, IRMA Lectures in Mathematics and Theoretical Physics 29, Eds V. A. Papadopoulos, EMS, Alberge (2019)

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Authors and Affiliations

  1. Department of Natural Resources Management and Agricultural Engineering, Agricultural University Athens, Iera Odos 55, 11855, Athens, Greece

    C. Charitos

  2. Department of Electrical and Computer Engineering, University of Western Makedonia, 50100, Kozani, Greece

    P. Dospra

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  1. C. Charitos
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  2. P. Dospra
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Correspondence to P. Dospra.

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Charitos, C., Dospra, P. Projections from surfaces of revolution in the Euclidean plane. Beitr Algebra Geom 62, 783–797 (2021). https://doi.org/10.1007/s13366-020-00542-3

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  • DOI: https://doi.org/10.1007/s13366-020-00542-3

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