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- W2466147029 abstract "We study a geometry associated with rank 3 distributions in dimension 8, whose symbol algebra is constant and has a simple Lie algebra sp(3,R) as Tanaka prolongation. We restrict our considerations to only those distributions that are defined in terms of a systems of ODEs of the form $dot{z}_{ij}=frac{partial^2 f(dot{x}_1,dot{x}_2)}{partial dot{x}_ipartial dot{x}_j}$, $ileq j=1,2$. For them we built the full system of local differential invariants, by solving an equivalence problem a'la Cartan, in the spirit of his 1910's five variable paper. The considered geometry is a parabolic geometry, and we show that its main invariant - the harmonic curvature - is a certain quintic. In the case when this quintic is maximally degenerate but nonzero, we use Cartan's reduction procedure and reduce the EDS governing the invariants to 11, 10 and 9 dimensions. As a byproduct all homogeneous models having maximally degenerate harmonic curvature quintic are found. They have symmetry algebras of dimension 11 (a unique structue), 10 (a 1-parameter family of nonequivalent structures) or 9 (precisely two nonequivalent structures)." @default.
- W2466147029 created "2016-07-22" @default.
- W2466147029 creator A5063787799 @default.
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- W2466147029 date "2016-06-28" @default.
- W2466147029 modified "2023-10-06" @default.
- W2466147029 title "Sp(3,R) Monge geometries in dimension 8" @default.
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- W2466147029 hasPublicationYear "2016" @default.
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