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Covariant and contravariant analytic self-adjoint vector fields. (English) Zbl 0574.53041

This paper generalizes, in some directions, the well-known Bochner theorem about the non-existence of analytic self-adjoint linear differential forms (or vector fields) on a compact Kähler manifold with positive (or negative) Ricci curvature. One of the main results says that if the Ricci form is everywhere semi-positive, and if n-k Ricci roots are positive in some open subset, then there exist at most k linearly independent analytic self-adjoint linear differential forms. The analogue of this result also holds, if we replace ”positive” by ”negative” everywhere, and the linear differential forms by vector fields.
Reviewer: O.Kowalski

MSC:

53C55 Global differential geometry of Hermitian and Kählerian manifolds
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