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.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 9, pp. 1231–1243, September, 2004.
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Sakharova, E., Yampol’skii, A. Powers of the curvature operator of space forms and geodesics of the tangent bundle. Ukr Math J 56, 1463–1480 (2004). https://doi.org/10.1007/s11253-005-0127-5
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DOI: https://doi.org/10.1007/s11253-005-0127-5