Studies of Some Curvature Operators in a Neighborhood of an Asymptotically Hyperbolic Einstein Manifold

✍ Scribed by Erwann Delay

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 122 KB
• Volume: 168
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.2001.2048

✦ Synopsis

On an asymptotically hyperbolic Einstein manifold (M, g 0 ) for which the Yamabe invariant of the conformal structure on the boundary at infinity is nonnegative, we show that the operators of Ricci curvature, and of Einstein curvature, are locally invertible in a neighborhood of the metric g 0 . We deduce in the C . case that the image of the Riemann-Christoffel curvature operator is a submanifold in a neighborhood of g 0 .