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We discuss irreducible decompositions of the curvature tensor in manifolds with special holonomy. The metrics considered are Kähler, Einstein, Calabi-Yau, Hyperkähler, Quaternionic Kähler and other special holonomy metrics. We will be using the following resources.

References:

1. Salamon, Simon. Riemannian geometry and holonomy groups.  Pitman Res. Notes Math. Ser., 201 Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989.