Characterization of the projections of geodesics of the Sasakian metric ofTCP n andT 1 CP n

Curves that are projections of geodesics of the Sasakian metric of the tangent and tangent sphere bundles of a complex projective space are considered. The main result is: THEOREM. If is a geodesic of TCPⁿ (T₁ CPⁿ) then ₀is a curve inCP ⁿ for which curvatures k₁, , k₅ are constant and k₆ = = k_2n = 0.Translated from Ukrainskii Geometricheskii Sbornik, No. 34, pp. 121–126, 1991.