an:05781300
Zbl 1212.53045
Ahmad, Abu-Saleem; Banaru, Mihail
Some applications of Kirichenko tensors
EN
An. Univ. Oradea, Fasc. Mat. 17, No. 2, 201-208 (2010).
00266607
2010
j
53C10
almost Hermitian structure; Nijenhuis tensor; Kirichenko tensors; Gray-Hervella classification; integrable structure
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.