Bitis, Gr. Covariant and contravariant analytic self-adjoint vector fields. (English) Zbl 0574.53041 Tensor, New Ser. 41, 204-209 (1984). 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 Cited in 1 Review MSC: 53C55 Global differential geometry of Hermitian and Kählerian manifolds Keywords:Kähler manifold; Ricci form; self-adjoint linear differential forms PDFBibTeX XMLCite \textit{Gr. Bitis}, Tensor, New Ser. 41, 204--209 (1984; Zbl 0574.53041)