Harmonic maps and the topology of conformally compact Einstein manifolds

Details Harmonic maps and the topology of conformally compact Einstein manifolds Harmonic maps and the topology of conformally compact Einstein manifolds

2001-12-03

arxiv.org/abs/math/0112023v1

Mathematics

Differential Geometry

To appear in Math. Res. Lett., 16 pages

Scientific paper

We study the topology of a complete asymptotically hyperbolic Einstein
manifold such that its conformal boundary has positive Yamabe invariant. We
proved that all maps from such manifold into any nonpositively curved manifold
are homotopically trivial. Our proof is based on a Bochner type argument on
harmonic maps.

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