Geodesic
The Manifold of Conformally Equivalent Metrics
Canadian journal of mathematics, Tome 29 (1977) no. 1, pp. 193-209

Voir la notice de l'article provenant de la source Cambridge University Press

Ebin [8] gives a thorough study of the space of riemannian metrics on a compact manifold M and of the action of the diffeomorphism group of M on . The purpose of this paper is to study the action of the larger group of conformorphisms, or conformai transformations, on and on . On , the L2-orthogonal decomposition induced by the action of gives a splitting of symmetric tensors into three summands introduced by York [25; 26]. We find submanifolds of tangent to the pieces of this decomposition. 
Fischer, Arthur E.; Marsden, Jerrold E. The Manifold of Conformally Equivalent Metrics. Canadian journal of mathematics, Tome 29 (1977) no. 1, pp. 193-209. doi: 10.4153/CJM-1977-019-x
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