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Geometry of 6-dimensional Hermitian manifolds of the octave algebra. (English. Russian original) Zbl 1365.53064
J. Math. Sci., New York 207, No. 3, 354-388 (2015); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 126 (2013).
This paper is a very useful survey of recent results in the geometry of 6-dimensional Hermitian manifolds of Cayley algebras. The author describes Gray-Hervella classes of almost Hermitian structures on 6-dimensional oriented submanifolds of Cayley algebras and proposes a characterization of these in terms of the Kirichenko tensors and the configuration tensor.
The author is a major contributor to this field, more than one third of the 188 References belong to himself. The article is divided into four sections:
1. Almost Hermitian structures on 6-dimensional oriented submanifolds of Cayley algebras.
2. Gray-Hervella classes of almost Hermitian structures on 6-dimensional oriented submanifolds of Cayley algebras.
3. Hermitian structures on 6-dimensional oriented submanifolds of Cayley algebras.
4. Approximately Kählerian structures on 6-dimensional oriented submanifolds of Cayley algebras.

MSC:
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53-02 Research exposition (monographs, survey articles) pertaining to differential geometry
Full Text: DOI
References:
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