On projectively equivalent metrics near points of bifurcation
نویسنده
چکیده
Let Riemannian metrics g and ḡ on a connected manifold Mn have the same geodesics (considered as unparameterized curves). Suppose the eigenvalues of one metric with respect to the other are all different at a point. Then, by the famous Levi-Civita’s Theorem, the metrics have a certain standard form near the point. Our main result is a generalization of Levi-Civita’s Theorem for the points where the eigenvalues of one metric with respect to the other bifurcate.
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