On the solvability of the transvection group of extrinsic symplectic symmetric spaces

Abstract

a b s t r a c tLet M be a symplectic symmetric space, and let ı : M → V be an extrinsic symplectic symmetric immersion in the sense of Krantz and Schwachhöfer (2010) [7], i.e., (V , Ω) is a symplectic vector space and ı is an injective symplectic immersion such that for each point p ∈ 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.