Rigidité conforme des hémisphères S^4_+ et S^6_+

Simon Raulot (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

Let (M,g) be a four or six dimensional compact Riemannian manifold which is locally conformally flat and assume that its boundary is totally umbilical. In this note, we prove that if the Euler characteristic of M is equal to 1 and if its Yamabe invariant is positive, then (M,g) is conformally isometric to the standard hemisphere. As an application and using a result of Hang-Wang, we prove a rigidity result for these hemispheres regarding the Min-Oo conjecture.

Mots clés: Manifolds with boundary; Hemisphere; Rigidity

Domaines: Géométrie différentielle [math.DG]

Simon Raulot. Rigidité conforme des hémisphères S^4_+ et S^6_+. Mathematische Zeitschrift, 2012, 271 (3-4), pp.707-714. ⟨10.1007/s00209-011-0885-8⟩. ⟨hal-00585754⟩