18 Aralık 2019,
İstanbul Teknik Üniversitesi Matematik Bölümü Seminerleri
Warped-like Product Manifolds with Spin(7) Holonomy
Ayşe Hümeyra Bilge
Kadir Has Üniversitesi, Türkiye
The group Spin7 is a subgroup of SO(8). An 8-manifolds is said to have Spin(7) holonomy, if the structure group of its principal bundle is reducible from SO(8) to Spin(7). These 8-manifolds are characterized by the existence of a closed self-dual, 4-form Ω, that is invariant under the action of the subgroup Spin(7). This 4-form is called the called the “Bonan form”.
If the 8-manifold has a product topology, the closedness of Ω gives restrictions on the metric. We consider 8-manifolds M = F1 × F2 × B with dimensions 3, 3 and 2, with a fibered structure. We prove that there are no non-trivial solutions if M is a product manifold, a warped product manifold or a multiply warped product. Non-trivial nontrivial solutions exist only in the case “warped-like manifolds”, that are characterized by a specific coupling between fibers and the base manifold.
Warped-like manifolds have been defined in [S.Uguz, Ph.D. Thesis], where it has been shown that if a 3 + 3 + 2 warped like manifolds admits a certain Bonan form is closed, then the 3-manifolds are 3-spheres. In that set-up, as a specific Bonan form is used, one cannot conclude the nonexistence of Spin(7) manifolds. In order to obtain non-existence results, we use the expression of the 7-parameter family of Bonan forms, the orbit of a given Bonan form under the action of SO(8) [AH. Bilge, T.Dereli, S.Kocak, 2009].
Geometri, Topoloji İngilizce
İTÜ Fen-Edebiyat Fakültesi B1-326
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