Topological properties of manifolds admitting a $Y^x$-Riemannian metric

@article{Chernov2010TopologicalPO,
title={Topological properties of manifolds admitting a \$Y^x\$-Riemannian metric},
author={V. Chernov and Paul Kinlaw and R. Sadykov},
journal={Journal of Geometry and Physics},
year={2010},
volume={60},
pages={1530-1538}
}

Abstract A complete Riemannian manifold ( M , g ) is a Y l x -manifold if every unit speed geodesic γ ( t ) originating at γ ( 0 ) = x ∈ M satisfies γ ( l ) = x for 0 ≠ l ∈ R . Berard-Bergery proved that if ( M m , g ) , m > 1 is a Y l x -manifold, then M is a closed manifold with finite fundamental group, and the cohomology ring H ∗ ( M , Q ) is generated by one element. We say that ( M , g ) is a Y x -manifold if for every ϵ > 0 there exists l > ϵ such that for every unit speed geodesic γ ( t… CONTINUE READING