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

Authors

  • Е. Sakharova
  • A. Yampolsky

Abstract

It is well known that if Г is a geodesic line of the tangent (sphere) bundle with Sasaki metric of a locally symmetric Riemannian manifold, then all geodesic curvatures of the projected curve λ=π 1463-01 Г are constant. In this paper, we consider the case of the tangent (sphere) bundle over real, complex, and quaternionic space forms and give a unified proof of the following property: All geodesic curvatures of the projected curve are zero beginning with k 3, k 6, and k 10 for the real, complex, and quaternionic space forms, respectively.

Published

25.09.2004

Issue

Section

Research articles

How to Cite

Sakharova Е., and A. Yampolsky. “Powers of the Curvature Operator of Space Forms and Geodesics of the Tangent Bundle”. Ukrains’kyi Matematychnyi Zhurnal, vol. 56, no. 9, Sept. 2004, pp. 1231-43, https://umj.imath.kiev.ua/index.php/umj/article/view/3837.