Vanishing theorem for irreducible symmetric spaces of noncompact type

Details Vanishing theorem for irreducible symmetric spaces of noncompact type Vanishing theorem for irreducible symmetric spaces of noncompact type

2006-09-28

arxiv.org/abs/math/0609822v1

Mathematics

Differential Geometry

10 pages

Scientific paper

We prove the following vanishing theorem. Let M be an irreducible symmetric
space of noncompact type whose dimension exceeds 2 and $M\ne SO_0(2,2)/SO(2)\tm
SO(2).$ Let E be any vector bundle over M, Then any E-valued $L^2$ harmonic
1-form over M vanishes. In particular we get the vanishing theorem for harmonic
maps from irreducible symmetric spaces of noncompact type.

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