On the projective geometry of paths
1937 ◽
Vol 5
(2)
◽
pp. 103-115
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Keyword(s):
An affine connection in an n-dimensional manifold Xn defines a system of paths, but conversely a connection is not defined uniquely by a system of paths. It was shown by H. Weyl that any two affine connections whose components are related by an equation of the formwhere is the unit affinor, give the same system of paths. In the geometry of a system of paths, a particular parameter on the paths, called the projective normal parameter, plays an important part. This parameter, which is invariant under a transformation of connection (1), was introduced by J. H. .C. Whitehead. It can be defined by means of a Schwarzian differential equation and it is determined up to linear fractional transformations. In § 1 this method is briefly discussed.
1968 ◽
Vol 64
(2)
◽
pp. 439-446
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1986 ◽
Vol 102
(3-4)
◽
pp. 253-257
◽
1964 ◽
Vol 4
(2)
◽
pp. 179-194
◽
1995 ◽
Vol 36
(4)
◽
pp. 438-459
◽
1963 ◽
Vol 3
(2)
◽
pp. 202-206
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Keyword(s):
1996 ◽
Vol 48
(4)
◽
pp. 871-886
◽
1998 ◽
Vol 35
(04)
◽
pp. 856-872
◽
1980 ◽
Vol 32
(6)
◽
pp. 1299-1305
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Keyword(s):