The Problem of Partial Geodesic Representation
نویسنده
چکیده
The original problem of geodesic representation, solved by Dini (1869) with reality restrictions and by Lie (1883) in complete generality, may be stated as follows : Find all pairs of surfaces S and Sx whose points may be put into correspondence in such a way that every geodesic on the one surface is pictured by a geodesic on the other. Apart from the trivial case where Sx is isometric with (applicable on) S, or with a surface homothetic to S, the only pairs of surfaces obtained belong to the Liouville class
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تاریخ انتشار 2010