Powers of the space forms curvature operator and geodesics of the tangent bundle

الأصل · EN

It is well-known that if a curve is a geodesic line of the tangent (sphere) bundle with Sasaki metric of a locally symmetric Riemannian manifold then the projected curve has all its geodesic curvatures constant. In this paper we consider the case of tangent (sphere) bundle over the real, complex and quaternionic space form and give a unified proof of the following property: all geodesic curvatures of projected curve are zero starting from k₃,k₆ and k₁₀ for the real, complex and quaternionic space formes respectively.