Low-dimensional totally geodesic submanifolds in "skew" position in the symmetric spaces of rank 2
classification
🧮 math.DG
keywords
complexgeodesicgrassmannianspositionskewsubmanifoldstotallycartan
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We use the Cartan representations of $SO(3)$ and $SU(3)$, and an irreducible 14-dimensional representation of $Sp(3)$ to construct certain totally geodesic submanifolds in "skew" position in the complex quadrics, the complex 2-Grassmannians and the quaternionic 2-Grassmannians.
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