One approach to parametric and adaptive model reduction is via the interpolation of
orthogonal bases, subspaces or positive definite system matrices. In all these cases, the …

The Grassmann manifold of linear subspaces is important for the mathematical modelling of
a multitude of applications, ranging from problems in machine learning, computer vision and …

In this paper, we study the gyrovector space structure (gyro-structure) of matrix manifolds.
Our work is motivated by the success of hyperbolic neural networks (HNNs) that have …

One approach to parametric and adaptive model reduction is via the interpolation of
orthogonal bases, subspaces or positive definite system matrices. In all these cases, the …

In this paper we investigate the existence and uniqueness of Riemannian cubics under
boundary conditions on position and velocity. We restrict the study to cubics close to …

The real symplectic Stiefel manifold is the manifold of symplectic bases of symplectic
subspaces of a fixed dimension. It features in a large variety of applications in physics and …

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The main objective of this paper is to propose a new method to generate smooth
interpolating curves on Stiefel manifolds. This method is obtained from a modification of the …

We address the problem of fitting parametric curves on the Grassmann manifold for the
purpose of intrinsic parametric regression. We start from the energy minimization formulation …

Deep neural networks (DNNs) on Riemannian manifolds have garnered increasing interest
in various applied areas. For instance, DNNs on spherical and hyperbolic manifolds have …