Extrinsically Immersed Symplectic Symmetric Spaces
Tom Krantz and Lorenz J. Schwachhöfer
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Submission date: 29. Sep. 2009
published in: Annals of global analysis and geometry, 37 (2010) 4, p. 379-391
DOI number (of the published article): 10.1007/s10455-009-9192-6
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Let be a symplectic vector space and let be a symplectic immersion. We show that is (locally) an extrinsic symplectic symmetric space (e.s.s.s.) in the sense of  if and only if the second fundamental form of is parallel.
Furthermore, we show that any symmetric space which admits an immersion as an e.s.s.s. also admits a full such immersion, i.e., such that is not contained in a proper affine subspace of V, and this immersion is unique up to affine equivalence.
Moreover, we show that any extrinsic symplectic immersion of M factors through to the full one by a symplectic reduction of the ambient space. In particular, this shows that the full immersion is characterized by having an ambient space V of minimal dimension.