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

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

2011-04-14

arxiv.org/abs/1104.2682v1

Mathematics

Differential Geometry

8 pages, to appear in Mathematische Zeitschrift

Scientific paper

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.

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