Jahnke, Priska; Radloff, Ivo Splitting jet sequences. (English) Zbl 1059.32004 Math. Res. Lett. 11, No. 2-3, 345-354 (2004). Here the author proves the following result which is an infinitesimal converse of a result of I. Biswas [J. Math. Pures Appl. 78, 1–26 (1999; Zbl 0921.53007)]: Let \(E\) be a holomorphic vector bundle on the compact Kähler manifold \(X\). Assume that the \(k\)-th jet sequence of \(E\) splits for some \(k>1\). Then \(X\) admits a holomorphic normal projective connection and the jet bundle \(J_{k-1}(E)\) admits a holomorphic connection. If \(\det(E)\) is not nef and either \(X\) is projective or it contains a rational curve, then \(X \cong P_n\) and \(E(1-k)\) is trivial. If \(\det(E)^\ast \equiv 0\), then \(X\) is covered by a torus and \(E\) admits a holomorphic affine connection. If \(\det(E)^\ast\) is ample, then \(X\) is covered by the unit ball. Reviewer: Edoardo Ballico (Povo) Cited in 1 Document MSC: 32Q15 Kähler manifolds 32L05 Holomorphic bundles and generalizations 58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) 58A20 Jets in global analysis Keywords:jet bundle; jet bundle of a vector bundle; splitting of a jet sequence; normal affine connection; normal projective connection Citations:Zbl 0921.53007 PDFBibTeX XMLCite \textit{P. Jahnke} and \textit{I. Radloff}, Math. Res. Lett. 11, No. 2--3, 345--354 (2004; Zbl 1059.32004) Full Text: DOI arXiv