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Vladimir S Matveev
Vladimir S Matveev
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I hope that my ``answer'' will not be understood solely as a propaganda of my survey http://arxiv.org/abs/1101.2069 where I discussed

(1) how, given geodesics, to reconstruct a connection (in both cases: when geodesics are parameterised and not parameterised)

(2) how, given a class od projectively related connections, to reconstruct a metric, and what are advantages of additional curvature assumptions on the metric

(3) what is the freedom in reconstructing the metric by geodesics -- in particular I proved the statement wellknown to experts and mentionen by Robert Bryant in his comment that for generic metric the geodesics determined, even unparameterized, determine the metric.

I hope that my ``answer'' will not be understood solely as a propaganda of my survey http://arxiv.org/abs/1101.2069 where I discussed

(1) how, given geodesics, to reconstruct a connection (in both cases: when geodesics are parameterised and not parameterised)

(2) how, given a class od projectively related connections, to reconstruct a metric, and what are advantages of additional curvature assumptions on the metric

(3) what is the freedom in reconstructing the metric by geodesics -- in particular I proved the statement wellknown to experts and mentionen by Robert Bryant in his comment that for generic metric the geodesics determined the metric.

I hope that my ``answer'' will not be understood solely as a propaganda of my survey http://arxiv.org/abs/1101.2069 where I discussed

(1) how, given geodesics, to reconstruct a connection (in both cases: when geodesics are parameterised and not parameterised)

(2) how, given a class od projectively related connections, to reconstruct a metric, and what are advantages of additional curvature assumptions on the metric

(3) what is the freedom in reconstructing the metric by geodesics -- in particular I proved the statement wellknown to experts and mentionen by Robert Bryant in his comment that for generic metric the geodesics, even unparameterized, determine the metric.

Source Link
Vladimir S Matveev
Vladimir S Matveev
  • 4.8k
  • 21
  • 31

I hope that my ``answer'' will not be understood solely as a propaganda of my survey http://arxiv.org/abs/1101.2069 where I discussed

(1) how, given geodesics, to reconstruct a connection (in both cases: when geodesics are parameterised and not parameterised)

(2) how, given a class od projectively related connections, to reconstruct a metric, and what are advantages of additional curvature assumptions on the metric

(3) what is the freedom in reconstructing the metric by geodesics -- in particular I proved the statement wellknown to experts and mentionen by Robert Bryant in his comment that for generic metric the geodesics determined the metric.