*-Ricci tensor *-Weyl curvature tensor 3-Sasakian manifold ??-space Clifford torus D’Atri space Einstein manifold Espais homogenis Kähler 2 Laplace operator Legendre curves Lie, Grups de Sasaki-Einstein Sasakian Lorentzian manifold compact Riemannian manifolds cost functional evolution dynamics finite-type formality generalized convexity geodesic chord property geodesic symmetries hadamard manifolds homogeneous Finsler space homogeneous geodesic homogeneous manifold homogeneous space hyperbolic space hypersphere inequalities