A general theory of surfaces and conjugate nets

A general theory of surfaces and conjugate nets
HTML articles powered by AMS MathViewer

by V. G. Grove

Trans. Amer. Math. Soc. 57 (1945), 105-122

DOI: https://doi.org/10.1090/S0002-9947-1945-0011582-7

PDF | Request permission

References

Philip O. Bell, Projective analogues of the congruence of normals, Amer. J. Math. 62 (1940), 680–686. MR 2236, DOI 10.2307/2371478
P. O. Bell, On differential geometry intrinsically connected with a surface element of projective arc length, Trans. Amer. Math. Soc. 50 (1941), 529–547. MR 5687, DOI 10.1090/S0002-9947-1941-0005687-0
G. M. Green, On the theory of curved surfaces, and canonical systems in projective differential geometry, Trans. Amer. Math. Soc. 16 (1915), no. 1, 1–12. MR 1500993, DOI 10.1090/S0002-9947-1915-1500993-7
Gabriel M. Green, Projective Differential Geometry of One-Parameter Families of Space Curves, and Conjugate Nets on a Curved Surface, Amer. J. Math. 38 (1916), no. 3, 287–324. MR 1506292, DOI 10.2307/2370453

Memoir on the general theory of surfaces and rectilinear congruences

V. G. Grove, A canonical form of Green’s projective analogue of the Gauss differential equations, Trans. Amer. Math. Soc. 32 (1930), no. 3, 473–484. MR 1501546, DOI 10.1090/S0002-9947-1930-1501546-5
V. G. Grove, On canonical forms of differential equations, Bull. Amer. Math. Soc. 36 (1930), no. 8, 582–586. MR 1561998, DOI 10.1090/S0002-9904-1930-05006-5

A tensor analysis for a

in a projective space

Projective differential geometry of curves and surfaces

Ernest Preston Lane, A Treatise on Projective Differential Geometry, University of Chicago Press, Chicago, Ill., 1942. MR 0007286
E. J. Wilczynski, Geometrical Significance of Isothermal Conjugacy of a Net of Curves, Amer. J. Math. 42 (1920), no. 4, 211–221. MR 1506415, DOI 10.2307/2370464