Lie Groups and their Lie-algebras, action of Lie groups on a smooth manifold, homogeneous spaces, Riemannian homogeneous spaces, the cannonical connection and Jacobi equations, two-point homogeneous spaces, Riemannian symmetric space, structure of orthogonal involutive Lie algebras, symmetric spaces and orthogonal involutive Lie algebras, curvature of symmetric spaces, Riemannian symmetric spaces of rank one.
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