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sydji
sydji
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Let $(T_1,g_1)$ and $(T_2,g_2)$ be two flat tori of dimension 2 such that their geodesic flows are $C^0$-conjugated, is there an isometry between $(T_1,g_1)$ and $(T_2,g_2)$ ?

I emphasize the fact that I ask a $C^0$-conjugacy. In the paper of Croke mentioned below in the answer it is a $C^1$-conjugacy.

Let $(T_1,g_1)$ and $(T_2,g_2)$ be two flat tori of dimension 2 such that their geodesic flows are $C^0$-conjugated, is there an isometry between $(T_1,g_1)$ and $(T_2,g_2)$ ?

Let $(T_1,g_1)$ and $(T_2,g_2)$ be two flat tori of dimension 2 such that their geodesic flows are $C^0$-conjugated, is there an isometry between $(T_1,g_1)$ and $(T_2,g_2)$ ?

I emphasize the fact that I ask a $C^0$-conjugacy. In the paper of Croke mentioned below in the answer it is a $C^1$-conjugacy.

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sydji
sydji
  • 31
  • 2

conjugacy between geodesic flows on 2-tori

Let $(T_1,g_1)$ and $(T_2,g_2)$ be two flat tori of dimension 2 such that their geodesic flows are $C^0$-conjugated, is there an isometry between $(T_1,g_1)$ and $(T_2,g_2)$ ?