87 citations · 877 across the 97 of their papers we have counts for
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math.DG1998★ 1 cited
Curvature of the Virasoro-Bott group
Peter W. Michor, Tudor Ratiu
We consider a natural Riemannian metric on the infinite dimensional manifold of all embeddings from a manifold into a Riemannian manifold, and derive its geodesic equation in the c…
chao-dyn1998★ 2 cited
The Euler-Poincare Equations and Semidirect Products with Applications to Continuum Theories
D. D. Holm, J. E. Marsden, T. S. Ratiu
We study Euler-Poincare systems (i.e., the Lagrangian analogue of Lie-Poisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Eul…