Geometry of the Symplectic Stiefel Manifold Endowed with the Euclidean Metric

@inproceedings{Gao2021GeometryOT,
  title={Geometry of the Symplectic Stiefel Manifold Endowed with the Euclidean Metric},
  author={Bin Gao and Nguyen Thanh Son and Pierre-Antoine Absil and Tatjana Stykel},
  booktitle={GSI},
  year={2021}
}
The symplectic Stiefel manifold, denoted by Sp(2p, 2n), is the set of linear symplectic maps between the standard symplectic spaces R and R. When p = n, it reduces to the well-known set of 2n × 2n symplectic matrices. We study the Riemannian geometry of this manifold viewed as a Riemannian submanifold of the Euclidean space R. The corresponding normal space and projections onto the tangent and normal spaces are investigated. Moreover, we consider optimization problems on the symplectic Stiefel… 
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