Non-closed isometry-invariant geodesics (Q292089)

Let \(M\) be a complete Riemannian manifold. The main goal of the paper is the following result: If there exists an \(A\)-invariant geodesic \(c\) for some isometry \(A\) of \(M\) then the geodesic flow line \(\dot{c}\) corresponding to \(c\) is dense in a \(k\)-dimentional torus \(N\) embedded in \(TM\). Moreover, each geodesic \(c_v\) with initial vector \(v\in N\) is also \(A\)-invariant. This is a starting point for a discussion about a Morse-Bott type theory for isometry-invariant geodesic problem.