2017
Том 69
№ 6

All Issues

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

Sakharova Е., Yampolsky A.

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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.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 9, pp 1463-1480.

Citation Example: Sakharova Е., Yampolsky A. Powers of the curvature operator of space forms and geodesics of the tangent bundle // Ukr. Mat. Zh. - 2004. - 56, № 9. - pp. 1231-1243.

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