Differential geometry of quasi-Sasakian manifolds
Sbornik. Mathematics, Tome 193 (2002) no. 8, pp. 1173-1201
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The full system of structure equations of a quasi-Sasakian structure is obtained. The structure of the main tensors on a quasi-Sasakian manifold (the Riemann–Christoffel tensor, the Ricci tensor, and other tensors) is studied on this basis. Interesting characterizations of quasi-Sasakian Einstein manifolds are obtained. Additional symmetry properties of the Riemann–Christoffel tensor are discovered and used for distinguishing a new class of $CR_1$ quasi-Sasakian manifolds. An exhaustive description of the local structure of manifolds in this class is given. A complete classification (up to the $\mathscr B$-transformation of the metric) is obtained for manifolds in this class having additional properties of the isotropy kind.
@article{SM_2002_193_8_a3,
author = {V. F. Kirichenko and A. R. Rustanov},
title = {Differential geometry of {quasi-Sasakian} manifolds},
journal = {Sbornik. Mathematics},
pages = {1173--1201},
publisher = {mathdoc},
volume = {193},
number = {8},
year = {2002},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2002_193_8_a3/}
}
V. F. Kirichenko; A. R. Rustanov. Differential geometry of quasi-Sasakian manifolds. Sbornik. Mathematics, Tome 193 (2002) no. 8, pp. 1173-1201. http://geodesic.mathdoc.fr/item/SM_2002_193_8_a3/