Latent Quaternionic Geometry
نویسنده
چکیده
In this article we discuss the interaction between the geometry of a quaternionKähler manifold M and that of the Grassmannian G3(g) of oriented 3-dimensional subspaces of a compact Lie algebra g. This interplay is described mainly through the moment mapping induced by the action of a group G of quaternionic isometries on M . We give an alternative expression for the endomorphisms I1, I2, I3, both in terms of the holonomy representation of M and the structure of the Grassmannian’s tangent space. A correspondence between the solutions of respective twistor-type equations on M and G3(g) is provided. MSC classification: 53C26; 53C35, 53C42, 53C28, 22E46, 57S25.
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