On the Solvability of the Transvection group of Extrinsic Symplectic Symmetric Spaces

Details On the Solvability of the Transvection group of Extrinsic Symplectic Symmetric Spaces On the Solvability of the Transvection group of Extrinsic Symplectic Symmetric Spaces

2010-11-24

arxiv.org/abs/1011.5340v1

Mathematics

Differential Geometry

15 pages

Scientific paper

Let $M$ be a symplectic symmetric space, and let $\imath : M \to V$ be an extrinsic symplectic symmetric immersion, i.e., $(V, \Omega)$ is a symplectic vector space and $\imath$ is an injective symplectic immersion such that for each point $p \in M$, the geodesic symmetry in $p$ is compatible with the reflection in the affine normal space at $\imath(p)$. We show that the existence of such an immersion implies that the transvection group of $M$ is solvable.

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