We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for a natural sub-Riemannian structure defined on Sasakian manifolds. This generalizes to arbitrary dimensions the corresponding three-dimensional results in [1, 5, 6] . 1 Introduction 916 2 Canonical frames and curvatures of a Jacobi curve 919 3 Sasakian manifolds and parallel adapted frames 920 4 Sub-Riemannian geodesic flows and Jacobi curves 923 5 Curvatures of sub-Riemannian geodesic flows 927 6 Conjugate time

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... timates & Bonnet-Myer's type theorem929 7 Model cases 934 8 Volume growth estimates 938 9 Laplacian comparison theorem 940 10 Appendix I 943 11 Appendix II 945 12 Appendix III 951 References 953