For any point $P$ on a sphere $S$, every line (geodesic?) containing $P$ is closed, i.e. wraps around $S$ and passes through $P$ "again."
1) Are there other objects besides spheres for which this property holds? Maybe a torus?
2) What tools would one use to do this type of analysis? For example, how would one prove for spheres that every line is a closed curve?
Thank you! Please feel free to correct my vocabulary or suggest some terminology, as I am new to the subject of non-Euclidean geometry.