منابع مشابه
Some remarks on G2-structures
This article consists of loosely related remarks about the geometry of G2structures on 7-manifolds, some of which are based on unpublished joint work with two other people: F. Reese Harvey and Steven Altschuler. After some preliminary background information about the group G2 and its representation theory, a set of techniques is introduced for calculating the differential invariants of G2-struc...
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We construct a family of compact 7-dimensional manifolds endowed with a weakly integrable generalized G2-structure with respect to a closed and non-zero 3-form. We relate the previous structures with SU(3)structures in dimension 7. Moreover, we investigate which types of SU(3)structures on a 6-dimensional manifold N give rise to a strongly integrable generalized G2-structure with respect to a n...
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An intrinsic metric tensor, a flat connexion and the corresponding distance-like function are constructed in the configuration space formed by the velocity field and the thermodynamic variables of an inviscid fluid. The kinetic-energy norm is obtained as a limiting case; all physical quantities are Galilean invariant. Explicit expressions are given for the case of an ideal gas. The flat connexi...
متن کاملYang-Mills flows on nearly Kähler manifolds and G2-instantons
We consider Lie(G)-valued G-invariant connections on bundles over spaces G/H , R×G/H and R2×G/H , where G/H is a compact nearly Kähler six-dimensional homogeneous space, and the manifolds R×G/H and R2×G/H carry G2and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on R×G/H is reduced to Newtonian mechanics of a particle moving in a plane with a q...
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Starting from a 6-dimensional nilpotent Lie group N endowed with an invariant SU(3) structure, we construct a homogeneous conformally parallel G2-metric on an associated solvmanifold. We classify all half-flat SU(3) structures that endow the rank-one solvable extension of N with a conformally parallel G2 structure. By suitably deforming the SU(3) structures obtained, we are able to describe the...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2008
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/han020