Abstract
In this chapter we give an overview of (locally) symmetric spaces and holonomy. Most standard results are proved or at least mentioned. We give a few explicit examples, including the complex projective space, in order to show how one can compute curvatures on symmetric spaces relatively easily. There is a brief introduction to holonomy and the de Rham decomposition theorem. We give a few interesting consequences of this theorem and then proceed to discuss how holonomy and symmetric spaces are related. Finally, we classify all compact manifolds with nonnegative curvature operator.
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