Special Warped-Like Product Manifolds with (Weak) G₂ Holonomy
By using fiber-base decomposition of the manifolds, the definition of warped-like product is considered as a generalization of multiply-warped product manifolds, by allowing the fiber metric to be not block diagonal. We consider (3 + 3 + 1) decomposition of 7-dimensional warped-like product manifo...
Gespeichert in:
| Datum: | 2013 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2013
|
| Schriftenreihe: | Український математичний журнал |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/165602 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Special Warped-Like Product Manifolds with (Weak) G₂ Holonomy / S. Uğuz // Український математичний журнал. — 2013. — Т. 65, № 8. — С. 1126–1140. — Бібліогр.: 36 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | By using fiber-base decomposition of the manifolds, the definition of warped-like product is considered as a generalization
of multiply-warped product manifolds, by allowing the fiber metric to be not block diagonal. We consider (3 + 3 + 1)
decomposition of 7-dimensional warped-like product manifolds, which is called a special warped-like product of the form
M = F × B, where the base B is a one-dimensional Riemannian manifold and the fibre F is of the form F = F₁ × F₂
where Fi, i = 1, 2, are Riemannian 3-manifolds. If all fibers are complete, connected, and simply connected, then the
fibers are isometric to S³ with constant curvature k > 0 in the class of special warped-like product metrics admitting the
(weak) G₂ holonomy determined by the fundamental 3-form. |
|---|