THE GEOMETRY OF THREE-FORMS IN SIX DIMENSIONS

By N. Hitchin. 2000

312 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/fb05f067008058965c289e71394cf7eac1a3a7d9

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Citations in the corpus

The intrinsic torsion of SU(3) and G_2 structures (2002, methodology): “In the general set-up, the SU(3) reduction leads to a splitting of the Nijenhuis tensor in two equal parts, which give rise to different components of the tensor τ2 on a 7-manifold M whose structure reduces from G2 to SU(3).”
Homogeneous nearly K\"{a}hler manifolds (2006, background): “However, in order to remain faithful to the point of view of differential forms adopted in this article we prefer the presentation by Hitchin [31] of this fact.”
Submanifolds of generalized complex manifolds (2003, background): “In [6], [7] it is assumed from the very beginning that generalized complex manifolds have even dimension (as real manifolds).”
Langlands duality and G2 spectral curves (2006, methodology): “As in [ 19 ] we define for a general three-form the linear transformation K by”
Six-Dimensional Solvmanifolds with Holomorphically Trivial Canonical Bundle (2014, methodology): “In Section 2 we consider the formalism of stable forms [17], together with ideas in [9, 14, 15, 28], and we explain in detail the method that we follow to classify unimodular solvable Lie algebras admitting a complex structure with non-zero closed (3,0)-form.”
Half‐flat structures and special holonomy (2009, background): “In fact, the corollary explicitly shows the equivalence of the two different definitions of ρ → ρ̂ given in [26, 27].”
Kähler Reduction of Metrics with Holonomy G2 (2003, background): “The authors are grateful to the referee for useful remarks, and to D. Conti for subsequent checking of some curvature computations.”
Short-time behaviour of a modified Laplacian coflow of G2-structures (2012, methodology): “Here we adapt the proof from [17] to show an analogous result for the functional V (ψ) on 4-forms.”
Six-Dimensional Nearly Kähler Manifolds of Cohomogeneity One (II) (2009, background): “[20,29]) that 3V can be divided into the following disjoint G-invariant sets: a G-invariant hypersurface ( 3V )0 = { P = 0 }, given by the zero set of a suitable relative G-invariant irreducible polynomial P of degree 4, and the complementary open sets”
Dirichlet Branes and Mirror Symmetry (2009, unknown): “For n = 6 and p = 3, ρ̂ is determined by the property that Ω = ρ+iρ̂ is a complex (3, 0)-form preserved by SL(3,C) [233].”
Stable forms and special metrics (2001, methodology): “ = d∗ρ = 0. Example: The case of n = 6 means that we have a complex closed locally decomposable 3-formρ+iρˆ. This yields the structure ofa complex 3-manifold with trivial canonical bundle as shown in [H]. The 8-dimensional case will occupy us next. 4 Eight-manifolds with PSU(3) structure Suppose tha”
Laplacian flow for closed G2 structures: Shi-type estimates, uniqueness and compactness (2015, background): “closed and has suﬃciently small torsion, then the ﬂow will exist for all time and converge to a torsion-free G2 structure. Another motivation for studying the Laplacian ﬂow comes from work of Hitchin [21] (see also [8]), which demonstrates its relationship to a natural volume functional. Let ¯ϕbe a ”
Generalized Calabi-Yau manifolds (2002, background): “The proof that it is integrable is the same as in [10] or [13] and holds generally for special (pseudo)-Kähler manifolds, of which U is an example.”