Decompositions of para-complex vector bundles and para-complex affine immersions
In this work, decompositions of para-complex and para-holomorphic vector bundles endowed with a connection over a para-complex manifold are studied. At first, the authors investigate connections and morphisms of para-holomorphic vector bundles. In particular, they prove that any connection with vanishing (0,2)-cuvature on a para-complex vector bundle \(E\) induces a unique para-holomorphic structure on \(E\). Then para-holomorphic decompositions are analyzed. Furthermore the authors introduce para-complex affine immersions and investigate decompositions induced by them. Finally, the above results are applied to obtain existence and uniqueness theorems for para-complex affine immersions.
scientific article; zbMATH DE number 5117898