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arXiv · 1011.5340

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

Lorenz J. Schwachhöfer
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Abstract

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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Lorenz J. Schwachhöfer. 2010-11-24. On the Solvability of the Transvection group of Extrinsic Symplectic Symmetric Spaces. https://doi.org/10.1016/j.geomphys.2011.05.012

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