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Quasigraphs

Published online by Cambridge University Press:  20 November 2018

Norman D. Lane ,
Peter Scherk  and
Jean M. Turgeon
Norman D. Lane
Affiliation:
McMaster University Hamilton, Ontario
Peter Scherk
Affiliation:
University of Toronto, Toronto, Ontario
Jean M. Turgeon
Affiliation:
Université de Montréal, Montréal, Québec
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Abstract

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In the study of direct differential geometry, families of oriented arcs and curves have been employed extensively to define the differentiability of an arc at a point in various kinds of planes; cf. [2]. In [6], P. Scherk used lines in the projective plane; in [3] and [4], N. D. Lane and P. Scherk used circles in the conformai plane; conic-sections in the projective plane were employed in [5] and [7] by N. D. Lane and K. D. Singh; in [1], M. Gupta and N. D. Lane used the graphs of polynomials of degree at most n in the affine plane.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 1 , 01 February 1977 , pp. 1 - 28
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Gupta, M. and Lane, N. D., Polynomial differentiability, order and characteristic, Journal of Geometry 3 (1973), 107–164.Google Scholar
2. Haupt, O. and H. Kùnneth, Geometrische Ordnungen (Springer Verlag, Berlin, 1967).Google Scholar
3. Lane, N. D. and Scherk, P., Differentiable points in the conformai plane, Can. J. Math. 5 (1953), 512–518.Google Scholar
4. Lane, N. D. and Scherk, P. Characteristic and order of differentiable points in the conformai plane, Trans. Amer. Math. Soc. 81 (1956), 358–378.Google Scholar
5. Lane, N. D. and Singh, K. D., Conical differentiation, Can. J. Math. 16 (1964), 169–190.Google Scholar
6. Scherk, P., Uber differenzierbare Kurven und Bogen I. Zum Begriff der Characteristik, Casopis Pest. Mat. 66 (1937), 165–171.Google Scholar
7. Singh, K. D. and Lane, N. D., Characteristic and order of conically differentiable points, J. Reine Angew. Math. 224 (1966), 164–184.Google Scholar