Ahmad, Abu-Saleem; Banaru, Mihail Some applications of Kirichenko tensors. (English) Zbl 1212.53045 An. Univ. Oradea, Fasc. Mat. 17, No. 2, 201-208 (2010). Summary: A short description of structural and virtual Kirichenko tensors that form a complete system of first-order differential-geometrical invariants of an arbitrary almost Hermitian structure is given. In two ways it is proved that an almost Hermitian structure is integrable if and only if its structural Kirichenko tensors vanish. A characterization of Gray-Hervella classes of almost Hermitian structures in terms of Kirichenko tensors is given. Cited in 13 Documents MSC: 53C10 \(G\)-structures Keywords:almost Hermitian structure; Nijenhuis tensor; Kirichenko tensors; Gray-Hervella classification; integrable structure PDF BibTeX XML Cite \textit{A.-S. Ahmad} and \textit{M. Banaru}, An. Univ. Oradea, Fasc. Mat. 17, No. 2, 201--208 (2010; Zbl 1212.53045)