## Normal fields of geodesic spheres

This question is related to this one (https://math.stackexchange.com/questions/1383511/normal-curvature-of-geodesic-spheres) I’ve asked at math.stackexchange. Let (M,g) be a compact Riemannian manifold with no conjugate points and (˜M,˜g) its universal covering. Let ˆg the Sasaki metric on TM−{0} and dˆg its associated distance function. Fix ˜p∈˜M and R=1. Let ˜H:=˜M−¯B1(p). For x∈˜H, consider the geodesic sphere centered at … Read more