M ar 2 00 6 Existence of closed G 2 - structures on 7 - manifolds
نویسنده
چکیده
In this note we propose a new way of constructing compact 7-manifolds with a closed G 2-structure. As a result we find a first example of a closed G 2-structure on S 3 × S 4. We also prove that any integral closed G 2-structure on a compact 7-manifold M 7 can be obtained by embedding M 7 to a universal space (W 3(80+8.C 3 8) , h). MSC: 53C10, 53C42 Key words: closed G 2-structures, submanifolds in semi-simple Lie groups, H-principle.
منابع مشابه
ar X iv : m at h / 02 08 19 7 v 1 [ m at h . D G ] 2 6 A ug 2 00 2 Hyperbolic Rank of Products
Generalizing [BrFa] we prove the existence of a bilipschitz embedded manifold of pinched negative curvature and dimension m1 +m2 −1 in the product X := Xm1 1 ×X m2 2 of two Hadamard manifolds Xmi i of dimension mi with pinched negative curvature. Combining this result with [BuySch] we prove the additivity of the hyperbolic rank for products of manifolds with pinched negative curvature.
متن کاملar X iv : 0 80 6 . 12 61 v 1 [ m at h . D G ] 7 J un 2 00 8 Dirac and Nonholonomic Reduction
Several aspects of Dirac reduction are compared and formulated from the same geometric point of view. A link with nonholonomic reduction is found. The theory of optimal momentum maps and reduction is extended from the category of Poisson manifolds to that of closed Dirac manifolds. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in det...
متن کاملar X iv : m at h / 05 04 08 2 v 4 [ m at h . D G ] 1 5 A pr 2 00 6 COMPLETE PROJECTIVE CONNECTIONS
The first examples of complete projective connections are uncovered: on surfaces, normal projective connections whose geodesics are all closed and embedded are complete. On manifolds of any dimension, normal projective connections induced from complete affine connections with slowly decaying positive Ricci curvature are complete.
متن کاملar X iv : 0 81 0 . 52 61 v 1 [ m at h . D G ] 2 9 O ct 2 00 8 Second order structures for sprays and connections on Fréchet manifolds
Ambrose, Palais and Singer [6] introduced the concept of second order structures on finite dimensional manifolds. Kumar and Viswanath [23] extended these results to the category of Banach manifolds. In the present paper all of these results are generalized to a large class of Fréchet mani-folds. It is proved that the existence of Christoffel and Hessian structures, connections, sprays and disse...
متن کاملar X iv : m at h / 06 11 50 4 v 1 [ m at h . G T ] 1 6 N ov 2 00 6 QUANTUM HYPERBOLIC GEOMETRY
We construct a new family, indexed by the odd integers N ≥ 1, of (2 + 1)-dimensional quantum field theories called quantum hyperbolic field theories (QHFT), and we study its main structural properties. The QHFT are defined for (marked) (2 + 1)-bordisms supported by compact oriented 3-manifolds Y with a properly embedded framed tangle LF and an arbitrary PSL(2,C)character ρ of Y \LF (covering, f...
متن کامل