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

Abstract

Let $M$ be a symplectic symmetric space, and let $ı:M\to V$ be an extrinsic symplectic symmetric immersion, i.e., $(V,\Omega )$ is a symplectic vector space and $ı$ 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 $ı(p)$. We show that the existence of such an immersion implies that the transvection group of $M$ is solvable.

15 pages

References in corpus (2)

• Tightness for a stochastic Allen--Cahn equation
• Extrinsic symplectic symmetric spaces