On Wasserstein geometry of Gaussian measures

<!-- *** Custom HTML *** --> The space of Gaussian measures on a Euclidean space is geodesically convex in the L²-Wasserstein space. This is a finite dimensional manifold since Gaussian measures are parameterized by means and covariance matrices. By restricting to the space of Gaussian measures inside the L²-Wasserstein space, we manage to provide detailed descriptions of the L²-Wasserstein geometry from a Riemannian geometric viewpoint. We obtain a formula for the sectional curvatures of the space of Gaussian measures, which is written out in terms of the eigenvalues of the covariance matrix.