On six-dimensional Vaisman — Gray submanifolds of the octave algebra
| Autor: | M. Banaru |
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| Jazyk: | English<br />Russian |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Дифференциальная геометрия многообразий фигур, Iss 50, Pp 29-35 (2019) |
| Druh dokumentu: | article |
| ISSN: | 0321-4796 2782-3229 |
| DOI: | 10.5922/0321-4796-2019-50-4 |
| Popis: | The W1 + W4 class of almost Hermitian manifolds (in accordance with the Gray — Hervella classification) is usually named as the class of Vaisman — Gray manifolds. This class contains all Kählerian, nearly Kählerian and locally conformal Kählerian manifolds. As it is known, Vaisman — Gray manifolds are invariant under the conformal transformations of the metric. A criterion in the terms of the configuration tensor for an arbitrary six-dimensional submanifold of Cayley algebra to belong to the Vaisman — Gray class of almost Hermitian manifolds is established. The Cartan structural equations of the almost contact metric structures induced on oriented hypersurfaces of six-dimensional Vaisman — Gray submanifolds of the octave algebra are obtained. It is proved that totally geodesic hypersurfaces of six-dimensional Vaisman — Gray submanifolds of Cayley algebra admit nearly cosymplectic structures (or Endo structures). This result is a generalization of the previously proved fact that totally geodesic hypersurfaces of nearly Kählerian manifolds also admit nearly cosymplectic structures. |
| Databáze: | Directory of Open Access Journals |
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