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Vector fields and flows on developable surfaces

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References

  • 1827 [1] Gauss, C. F., Disquisitiones generales circa superficies curvas. Collected papers Vol. 4, 217–258.

    Google Scholar 

  • 1837 [1] Earnshaw, S., On fluid motion, so far as it is expressed by the equation of continuity. Transactions of the Cambridge Philosophical Society 6, 203–233.

    Google Scholar 

  • 1856 [1] Mainardi, G., Istituto Lombardo di scienze e lettere, Milan Giornale ... e biblioteca Italiana 9, 360.

    Google Scholar 

  • 1861 [1] Weingarten, J., Über eine Klasse aufeinander abwickelbarer Flächen. Journal für die reine und angewandte Mathematik (Crelle) 59, 382–393.

    Google Scholar 

  • 1868 [1] Codazzi, D., Annali di matematica pura e applicata 2, 273.

    Google Scholar 

  • 1871 [1] Beltrami, E., Sui principi fondamentali della idrodinamica. Memorie, Accademia delle Scienze dell' Istituto di Bologna (3) 1, 431–476; 2 (1872), 381–437; 3 (1873), 349–407; 5 (1874), 443–484=Richerche sulla cinematica dei fluidi, Opere 2, 202–379.

    Google Scholar 

  • 1925 [1] Levi-Civita, T., Lezioni di Calcolo Differenziale Assoluto. Roma.

  • 1927 [1] Masotti, A., Decomposizione intrinseca del vortice e sue applicazioni. Istituto Lombardo di Scienze e Lettere, Rendiconti (2), 60, 869–874.

    Google Scholar 

  • 1927 [2] Weatherburn, C. E., Differential Geometry of Three Dimensions. Cambridge.

  • 1930 [1] Weatherburn, C. E., Differential Geometry of Three Dimensions, Volume II. Cambridge.

  • 1934 [1] Struik, D. J., Theory of Linear Connections. Berlin: Springer.

    Google Scholar 

  • 1936 [1] Vranceanu, M. G., Les espaces non holonomes et leurs applications mécaniques. Mémorial des sciences mathématiques, no. 76.

  • 1943 [1] Sommerville, D. M. Y., Analytical Geometry of Three Dimensions. Cambridge.

  • 1947 [1] Brand, L., Vector and Tensor Analysis. New York: John Wiley.

    Google Scholar 

  • 1951 [1] Bjørgum, O., On Beltrami vector fields and flows, Part 1. Universitet I Bergen, Årbok 1951, Naturvitenskapelig rekke nr. 1.

  • 1951 [2] Schouten, J. A., Tensor Analysis for Physicists. Oxford: Clarendon.

    Google Scholar 

  • 1954 [1] Schouten, J. A., Ricci-Calculus, Second Edition. Berlin-Göttingen-Heidelberg: Springer.

    Google Scholar 

  • 1954 [2] Truesdell, C., The Kinematics of Vorticity. Bloomington: Indiana University Press.

    Google Scholar 

  • 1959 [1] Kreyszig, E., Differential Geometry. University of Toronto Press.

  • 1966 [1] Yih, C-S, On the Earnshaw conjecture. Zeitschrift für angewandte Mathematik und Mechanik 46, 7, 471–472.

    Google Scholar 

  • 1967 [1] Marris, A. W., Vector fields of solenoidal vector-line rotation. Arch. Rational Mech. Anal. 27, 195–232.

    Google Scholar 

  • 1968 [1] Marris, A. W., & S. L. Passman, Generalized circulation-preserving flows. Arch. Rational Mech. Anal. 28, 245–264.

    Google Scholar 

  • 1969 [1] Marris, A. W., Addendum to “Vector fields of solenoidal vector-line rotation” (Vol. 27, No. 3, p. 195–232, 1967). A class of permanent flows of solenoidal vector-line rotation. Arch. Rational Mech. Anal., forthcoming.

    Google Scholar 

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Communicated by C. Truesdell

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Marris, A.W., Passman, S.L. Vector fields and flows on developable surfaces. Arch. Rational Mech. Anal. 32, 29–86 (1969). https://doi.org/10.1007/BF00253256

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