Existence of symplectic 3-forms of G2-type or G̃2-type on 7-manifolds
نویسنده
چکیده
In this note we consider the existence problem for symplectic 3forms of G2-type or G̃2-type on 7-manifolds. We find a first example of a closed G̃2-structure on S 3 × S4. We also prove that any integral symplectic 3-forms on a compact 7-manifold M7 can be obtained by embedding M7 to a universal space (W 3(80+8.C 3 8 ), h). MSC: 53C10, 53C42
منابع مشابه
The existence of symplectic 3-forms on 7-manifolds
A k-form ω is called multi-symplectic, if Iω is a monomorphism. The classification (under the action ofGl(V )) of multi-symplectic 3-forms in dimension 7 has been done by Bures and Vanzura [B-V2002]. There are together 8 types of these forms, among them there two generic classes of G2-form ω 3 1 and G̃2-form ω 3 2 . They are generic in the sense of Gl(V )-action, more precisely the orbits Gl(V )...
متن کاملExistence of symplectic 3-forms on 7-manifolds
In this note we consider the existence problem for symplectic 3forms on 7-manifolds. We find a first example of a closed 3-form of G̃2-type on S 3 × S4. We also prove that any integral symplectic 3forms on a compact 7-manifold M7 can be obtained by embedding M7 to a universal space (WN , h), where N = N0 +3(80 + 8.C 3 8 )), the number N0 does not depend on M 7. MSC: 53C10, 53C42
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تاریخ انتشار 2006