Vector fields and flows on developable surfaces. (English) Zbl 0167.54601
Keywords:
fluid mechanicsReferences:
| [1] | 1827 [1] Gauss, C. F., Disquisitiones generales circa superficies curvas. Collected papers Vol. 4, 217–258. · JFM 31.0599.11 |
| [2] | 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. |
| [3] | 1856 [1] Mainardi, G., Istituto Lombardo di scienze e lettere, Milan Giornale ... e biblioteca Italiana 9, 360. |
| [4] | 1861 [1] Weingarten, J., Über eine Klasse aufeinander abwickelbarer Flächen. Journal für die reine und angewandte Mathematik (Crelle) 59, 382–393. · doi:10.1515/crll.1861.59.382 |
| [5] | 1868 [1] Codazzi, D., Annali di matematica pura e applicata 2, 273. |
| [6] | 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. |
| [7] | 1925 [1] Levi-Civita, T., Lezioni di Calcolo Differenziale Assoluto. Roma. · JFM 51.0565.20 |
| [8] | 1927 [1] Masotti, A., Decomposizione intrinseca del vortice e sue applicazioni. Istituto Lombardo di Scienze e Lettere, Rendiconti (2), 60, 869–874. · JFM 53.0788.08 |
| [9] | 1927 [2] Weatherburn, C. E., Differential Geometry of Three Dimensions. Cambridge. · JFM 53.0658.08 |
| [10] | 1930 [1] Weatherburn, C. E., Differential Geometry of Three Dimensions, Volume II. Cambridge. · JFM 56.0589.01 |
| [11] | 1934 [1] Struik, D. J., Theory of Linear Connections. Berlin: Springer. · Zbl 0008.08402 |
| [12] | 1936 [1] Vranceanu, M. G., Les espaces non holonomes et leurs applications mécaniques. Mémorial des sciences mathématiques, no. 76. |
| [13] | 1943 [1] Sommerville, D. M. Y., Analytical Geometry of Three Dimensions. Cambridge. · Zbl 0008.40203 |
| [14] | 1947 [1] Brand, L., Vector and Tensor Analysis. New York: John Wiley. · Zbl 0032.30602 |
| [15] | 1951 [1] Bjørgum, O., On Beltrami vector fields and flows, Part 1. Universitet I Bergen, Årbok 1951, Naturvitenskapelig rekke nr. 1. |
| [16] | 1951 [2] Schouten, J. A., Tensor Analysis for Physicists. Oxford: Clarendon. · Zbl 0044.38302 |
| [17] | 1954 [1] Schouten, J. A., Ricci-Calculus, Second Edition. Berlin-Göttingen-Heidelberg: Springer. |
| [18] | 1954 [2] Truesdell, C., The Kinematics of Vorticity. Bloomington: Indiana University Press. · Zbl 0056.18606 |
| [19] | 1959 [1] Kreyszig, E., Differential Geometry. University of Toronto Press. |
| [20] | 1966 [1] Yih, C-S, On the Earnshaw conjecture. Zeitschrift für angewandte Mathematik und Mechanik 46, 7, 471–472. · doi:10.1002/zamm.19660460713 |
| [21] | 1967 [1] Marris, A. W., Vector fields of solenoidal vector-line rotation. Arch. Rational Mech. Anal. 27, 195–232. · Zbl 0173.27603 · doi:10.1007/BF00290613 |
| [22] | 1968 [1] Marris, A. W., & S. L. Passman, Generalized circulation-preserving flows. Arch. Rational Mech. Anal. 28, 245–264. · Zbl 0181.54101 · doi:10.1007/BF00251809 |
| [23] | 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. · Zbl 0173.27603 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
