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MATH 673

Lie Groups and Symmetric Spaces

3 hours

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.

Recommended Books:

 1)  F.W. Warner, Foundations of differentiable manifolds and Lie groups, Scot Foresman and Company, 1971

2) John Milnor, Curvatures of left invariant metrics on lie groups, Advances in Math. 21(3) (1976), 293-329.

3) Gerard Walschap, Geometric vector fields on Lie groups, Diff. Geom. Appl. 7(3) (1997), 219-230.

 

 

 M-673

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