TITLE: Jacobi fields on non-symmetric spaces
QUESTION [5 upvotes]: I am searching for examples of manifolds which are not symmetric spaces but where Jacobi fields can be computed in closed form. For now, I am aware of

Gaussian distribution with the Wasserstein metric: https://arxiv.org/pdf/2012.07106.pdf
Kendall shape space: https://arxiv.org/pdf/1906.11950.pdf

Are there many others? Thank you for your help.

REPLY [3 votes]: Damek-Ricci spaces are obtained by equipping certain solvable Lie groups with appropriate invariant Riemannian metrics. This class is larger than the class of symmetric spaces (this was precisely the point of their construction as counterexamples to the Lichnerowicz conjecture ), and the Jacobi fields on them are explicitly described in Section 4.2 of Isoparametric hypersurfaces in Damek–Ricci spaces by Díaz-Ramos and Domínguez-Vázquez.