A general theory of surfaces and conjugate nets

Author:
V. G. Grove

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

MSC:
Primary 53.0X

MathSciNet review:
0011582

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References | Similar Articles | Additional Information

**[1]**Philip O. Bell,*Projective analogues of the congruence of normals*, Amer. J. Math.**62**(1940), 680–686. MR**0002236****[2]**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**0005687**, 10.1090/S0002-9947-1941-0005687-0**[3]**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**, 10.1090/S0002-9947-1915-1500993-7**[4]**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**, 10.2307/2370453**[5]**-,*Memoir on the general theory of surfaces and rectilinear congruences*, Trans. Amer. Math. Soc. vol. 20 (1919) pp. 80-153.**[6]**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**, 10.1090/S0002-9947-1930-1501546-5**[7]**V. G. Grove,*On canonical forms of differential equations*, Bull. Amer. Math. Soc.**36**(1930), no. 8, 582–586. MR**1561998**, 10.1090/S0002-9904-1930-05006-5**[8]**-,*A tensor analysis for a**in a projective space*, Bull. Amer. Math. Soc. vol. 45 (1939) pp. 385-398.**[9]**E. P. Lane,*Projective differential geometry of curves and surfaces*, The University of Chicago Press, 1932.**[10]**Ernest Preston Lane,*A Treatise on Projective Differential Geometry*, University of Chicago Press, Chicago, Ill., 1942. MR**0007286****[11]**E. J. Wilczynski,*Geometrical Significance of Isothermal Conjugacy of a Net of Curves*, Amer. J. Math.**42**(1920), no. 4, 211–221. MR**1506415**, 10.2307/2370464

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

Article copyright:
© Copyright 1945
American Mathematical Society