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Mathematics
Differential Geometry
How to calculate Riemannian Metric by distance function?
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[QUOTE="Fangyang Tian, post: 3856903, member: 407228"] [b]How to calculate Riemannian Metric by distance function??[/b] Dear Folks: Here is the problem: in |z|<1, we difine a distance between any two points z[SUB]1[/SUB] and z[SUB]2[/SUB] by d(z[SUB]1[/SUB] , z[SUB]2[/SUB]) = ln((z[SUB]1[/SUB] - b)(z[SUB]2[/SUB] - a)/((z[SUB]1[/SUB] - a)(z[SUB]2[/SUB] - b))) ,where a is the intersection of line z[SUB]1[/SUB]z[SUB]2[/SUB] and the circle which is nearer to z[SUB]1[/SUB], and b is the other intersection. How to compute the Remannian Metric ds[SUP]2[/SUP]. My classmates calculated it indirectly for he knew the background of the problem?? But is there a direct way?? Many thanks! [/QUOTE]
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Mathematics
Differential Geometry
How to calculate Riemannian Metric by distance function?
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