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Geodesically equivalent metrics on homogenous spaces

Neda Bokan; Tijana Šukilović; Srdjan Vukmirović — 2019

Czechoslovak Mathematical Journal

Two metrics on a manifold are geodesically equivalent if the sets of their unparameterized geodesics coincide. We show that if two $G$ -invariant metrics of arbitrary signature on homogenous space $G / H$ are geodesically equivalent, they are affinely equivalent, i.e. they have the same Levi-Civita connection. We also prove that the existence of nonproportional, geodesically equivalent, $G$ -invariant metrics on homogenous space $G / H$ implies that their holonomy algebra cannot be full. We give an algorithm for...

Visualization of the Lobachevskian Plane

Ilija Knezević; Radmila Sazdanović; Srdjan Vukmirović — 2002

Visual Mathematics

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