The geometry of three-forms in six dimensions.

DOI10.4310/jdg/1090341263zbMath1036.53042arXivmath/0010054OpenAlexW1534745613WikidataQ115203098 ScholiaQ115203098MaRDI QIDQ1609792

Nigel J. Hitchin

Publication date: 15 August 2002

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0010054

zbMATH Keywords

moduli space pseudo-Kähler structure differential three-forms self-duality of 3-forms

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Moduli problems for differential geometric structures (58D27) Differential geometric aspects of harmonic maps (53C43)

Related Items

Modified Laplacian coflow of $G_{2}$-structures on manifolds with symmetry, Generalised geometry for string corrections, $\mathrm{Spin}(7)$-manifolds in compactifications to four dimensions, Classification of real trivectors in dimension nine, Enhanced supersymmetry from vanishing Euler number, A non Ricci-flat Einstein pseudo-Riemannian metric on a 7-dimensional nilmanifold, Infinitesimal moduli of G2 holonomy manifolds with instanton bundles, M-theory potential from the $G_{2}$ Hitchin functional in superspace, Yang-Mills solutions and $\mathrm{Spin}(7)$-instantons on cylinders over coset spaces with $G_2$-structure, Gauged supergravities from M-theory reductions, The infinitesimal moduli space of heterotic $G_2$ systems, 6D fractional quantum Hall effect, $N=1$ supercurrents of eleven-dimensional supergravity, Asymmetric orbifolds, non-geometric fluxes and non-commutativity in closed string theory, Constrained systems, generalized Hamilton-Jacobi actions, and quantization, The gauge dual of Romans mass, Coupled $\mathrm{SU}(3)$-structures and supersymmetry, Half-flat structures on indecomposable Lie groups, On Hodge theory for the generalized geometry. I, Geometric structures associated with a simple Cartan 3-form, Twistorial eigenvalue estimates for generalized Dirac operators with torsion, An elliptic boundary value problem for $G_{2}$-structures, Superpotential of three dimensional $\mathcal{N} = 1$ heterotic supergravity, Toric nearly Kähler manifolds, Coclosed $\mathrm{G}_{2}$-structures inducing nilsolitons, U-dual fluxes and generalized geometry, $S^1$-quotient of $\mathrm{Spin}(7)$-structures, New potentials from Scherk-Schwarz reductions, An invitation to multisymplectic geometry, Einstein warped $\mathrm{G}_{2}$ and spin(7) manifolds, Meromorphic flux compactification, $L^2$ harmonic forms on complete special holonomy manifolds, Probing the string winding sector, On almost complex structures on six-dimensional products of spheres, Hermitian curvature flow, Half-flat structures on decomposable Lie groups, The Hitchin functionals and the topological $B$-model at one loop, Soliton solutions for the Laplacian co-flow of some $G_2$-structures with symmetry, Symplectic half-flat solvmanifolds, Conical Ricci-flat nearly para-Kähler manifolds, Eleven-dimensional supergravity in 4D, $N=1$ superspace, Short-time behaviour of a modified Laplacian coflow of $G_2$-structures, A new equation on the Calabi-Yau metrics in low dimensions, Marginal deformations of 3d $ \mathcal{N}=2 $ CFTs from $\mathrm{AdS}_{4}$ backgrounds in generalised geometry, Half-flat structures on products of three-dimensional Lie groups, Hypersymplectic 4-manifolds, the $G_2$-Laplacian flow, and extension assuming bounded scalar curvature, Five-brane superpotentials, blow-up geometries and $SU(3)$ structure manifolds, $\mathcal{N}=1 $ vacua in exceptional generalized geometry, Instantons on the exceptional holonomy manifolds of Bryant and Salamon, Supersymmetric configurations, geometric transitions and new non-Kähler manifolds, On supersymmetric $ \mathrm{AdS}_4$ orientifold vacua, Local curvature estimates for the Laplacian flow, Homogeneous symplectic half-flat 6-manifolds, Calabi-Yau manifolds and SU(3) structure, The twistor space of a dimensional almost Hermitian manifold, Flat nearly Kähler manifolds, Components of eleven-dimensional supergravity with four off-shell supersymmetries, The EFT stringy viewpoint on large distances, $G_{2}$-structures and octonion bundles, Curvature decomposition of $G_2$-manifolds, Effective action from M-theory on twisted connected sum $G_2$-manifolds, Laplacian flow for closed $\mathrm{G}_{2}$ structures: Shi-type estimates, uniqueness and compactness, Quantum corrections in string compactifications on $\mathrm{SU}(3)$ structure geometries, Partial supergravity breaking and the effective action of consistent truncations, Type IIB flux vacua from G-theory. I, Type IIB flux vacua from G-theory. II, The Laplacian coflow on almost-abelian Lie groups, A CR twistor space of a $G_{2}$-manifold, Integral geometry under $G_2$ and $Spin(7)$, Manifolds with parallel differential forms and Kähler identities for $G_{2}$-manifolds, Cocalibrated structures on Lie algebras with a codimension one Abelian ideal, Six-dimensional nearly Kähler manifolds of cohomogeneity one. II, Half-flat nilmanifolds, Compatible structures on Lie algebroids and Monge-Ampère operators, Hitchin's equations and $M$-theory phenomenology, The geometry of special symplectic representations, Mirror symmetry and generalized complex manifolds. I: The transform on vector bundles, spinors, and branes, $G_2$-structures with torsion from half-integrable nilmanifolds, Flux compactification on smooth, compact three-dimensional toric varieties, Generalized gauge theories with nonunitary parallel transport: * general relativity with cosmological constant as an example, Generalising $G_2$ geometry: involutivity, moment maps and moduli, Complex solutions of Monge-Ampère equations, On quartic double fivefolds and the matrix factorizations of exceptional quaternionic representations, Symmetries of $\mathcal{N} = (1, 0)$ supergravity backgrounds in six dimensions, $\operatorname{SO}(3)$-invariant $G_2$-cobordisms, Local geometry of the $G_{2}$ moduli space, Heterotic domain wall solutions and $\mathrm{SU}(3)$ structure manifolds, Closed $\mathrm{SL}(3,\mathbb{C})$-structures on nilmanifolds, Laplacian coflow for warped $G_2$-structures, The Laplacian flow of locally conformal calibrated $\operatorname{G}_{2}$-structures, Complete noncompact $\mathrm{G}_2$-manifolds from asymptotically conical Calabi-Yau 3-folds, $S^1$-invariant Laplacian flow, Estimates and Monotonicity for a heat flow of isometric $G_2$-structures, An extension of the Siegel space of complex abelian varieties and conjectures on stability structures, Topological $G_2$ and Spin(7) strings at 1-loop from double complexes, Quantum entropy of BMPV black holes and the topological M-theory conjecture, Closed $\operatorname{G}_2$-eigenforms and exact $\operatorname{G}_2$-structures, Bochner-Kodaira formulas and the type IIA flow, Cones of $G$ manifolds and Killing spinors with skew torsion, On the existence of balanced metrics on six-manifolds of cohomogeneity one, Unnamed Item, Classification of compact homogeneous spaces with invariant G2-structures, Unnamed Item, COMPLEX CAYLEY STRUCTURES ON SPHERES S2,4 AND S3,3., LEFT-INVARIANT ALMOST PARA-HERMITIAN STRUCTURES ON SOME SIX-DIMENSIONAL NILPOTENT LIE GROUPS, Classification of $k$-forms on ${\bf R}^n$ and the existence of associated geometry on manifolds, A compact $\mathrm G_2$-calibrated manifold with first Betti number $b_1 = 1$, Unnamed Item, The energy functional of $G_2$-structures compatible with a background metric, Framed M-branes, corners, and topological invariants, On the boundary behavior of left-invariant Hitchin and hypo flows, Symmetries, tensors, and the Horrocks bundle, Purely coclosed G₂‐structures on nilmanifolds, The Coulomb gauge in non-associative gauge theory, Closed ${G_2}$-structures on compact quotients of Lie groups, Einstein metrics on bundles over Hyperkähler manifolds, Degenerate multilinear forms and Hermitian and para-Hermitian structures, Reductive homogeneous spaces of the compact Lie group $G_2$, Closed 3‐forms in five dimensions and embedding problems, Maximally twisted eleven-dimensional supergravity, Quantum Chern-Simons theories on cylinders: BV-BFV partition functions, Topological field theories of 2- and 3-forms in six dimensions, Six dimensional homogeneous spaces with holomorphically trivial canonical bundle, CR-twistor spaces over manifolds with $G_2$- and spin(7)-structures, Geometric flows and supersymmetry, Isometric flows of $G_2$-structures, Dynamics of 3-forms in seven dimensions, Introduction to $$\mathrm {G}_2$$ Geometry, Geometric Flows of $${{\,\mathrm{G\!}\,}}_2$$ Structures, On G$$_{\mathbf 2}$$-Structures, Special Metrics and Related Flows, Laplacian Flow for Closed $$\mathrm{G}_2$$ Structures, Flows of Co-closed $$G_{2}$$-Structures, 6D Interpretation of 3D Gravity, A geometric interpretation of coherent structures in Navier–Stokes flows, COMPOSITION ALGEBRAS AND THE TWO FACES OF G₂, Calibrated subbundles in noncompact manifolds of special holonomy, Stringy domain walls of $N=1$, $D=4$ supergravity, Einstein locally conformal calibrated $G_2$-structures, Lifting $SU(3)$-structures to nearly parallel $G_2$-structures, Deformations of compact coassociative 4-folds with boundary, Unnamed Item, Conformal transformations of the pseudo‐Riemannian metric of a homogeneous pair, G₂-structures forN = 1 supersymmetric AdS₄solutions ofM-theory, ON THE MASLOV INDEX OF LAGRANGIAN SUBMANIFOLDS OF GENERALIZED CALABI–YAU MANIFOLDS, Topological M-theory, self-dual gravity and the Immirzi parameter, Unnamed Item, Observations on BPS observables in 6D

Cites Work