Latent Quaternionic Geometry

Details Latent Quaternionic Geometry Latent Quaternionic Geometry

2006-04-10

arxiv.org/abs/math/0604219v1

Mathematics

Differential Geometry

30 pages

Scientific paper

In this article we discuss the interaction between the geometry of a quaternion-Kahler manifold M and that of the Grassmannian G(3,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 I_{1},I_{2},I_{3}, 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 G(3,g) is provided.

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