Review of recent G₂-structures on 7D manifolds.
problem Constructing examples of closed G₂-structures.
method Discussion of recent results and examples.
result Review of recent findings on G₂-structures.
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17 results for “7D”
Study local control in a 7D quaternionic Heisenberg group.
problem Optimizing geodesics in a 7D quaternionic Heisenberg group.
method Matrix representation and analysis of sub-Riemannian structure symmetries.
result Impact of symmetries on geodesic optimality.
Investigates CR structures in 7D, showing 8 is max symmetry dimension.
problem CR structures in 7D with intransitive symmetry.
method Various methods to bound symmetry dimension, demonstrating existence of non-equivalent models.
result Existence of infinitely many non-equivalent submaximally symmetric models.
Researchers found a non-Ricci-flat Einstein metric on a 7D nilpotent Lie group.
problem Existence of Einstein metrics on 7D nilpotent Lie algebras.
method Constructed a left-invariant pseudo-Riemannian metric on a 7D nilpotent Lie group.
result Found a non-Ricci-flat Einstein metric on a 7D nilpotent Lie group.
Study on structures and almost para-contact structures in 7D.
problem Understanding the relation between structures and almost para-contact structures.
method Calculating projections using properties of structures.
result Determined the class of almost para-contact structures induced by structures.
On 7D quaternionic contact manifolds, eigenvalue bounds imply special structure.
problem Eigenvalue bounds on quaternionic contact manifolds.
method Lower Ricci curvature bound and non-negative -function.
result Eigenvalue is smallest if and only if manifold is qc-Einstein.
Classifies 7D manifolds with specific geometric properties.
problem Classifying 7D manifolds with parallel skew-symmetric torsion and holonomy.
method Extending Friedrich's work, using classification techniques for naturally reductive spaces and nearly parallel -structures.
result Complete classification of 7D manifolds with the specified properties.
Study on CR structures in 7D, proving maximal symmetry dimension.
problem Proving symmetry dimension bound for CR structures in 7D.
method Investigating homogeneous models and proving uniqueness.
result 8 is the maximal symmetry dimension of 3-nondegenerate CR structures in 7D.
Study shows a copy of 7D real projective space in the space of almost complex structures on 6-sphere.
problem Understanding the topology of almost complex structures on the 6-sphere.
method Analyzes the fundamental and rational homotopy groups, computes homotopy fiber and groups, and generalizes to 6-manifolds.
result Induces isomorphism on fundamental and rational homotopy groups of the 6-sphere.
Study of flows on 7D manifolds with holomorphic properties.
problem Characterizing transversely holomorphic partially hyperbolic flows.
method Analyzing flows with biholomorphic holonomy pseudo-group, proving properties under integrable subcenter distribution.
result Flow projects to a transversely holomorphic Anosov flow on a 5D manifold.
The paper confirms a conjecture for 3D manifolds and extends it to 3-7D under specific conditions.
problem Confirming a conjecture about asymptotically flat Riemannian manifolds with nonnegative scalar curvature.
method Analyzing limits of isoperimetric surfaces to extend a 3D result to higher dimensions.
result The conjecture holds for 3D and is extended to 3-7D under certain conditions.
In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. We show that a gradient descent algorithm with initial value obtained from a spectral method can, in particular, reconstruct a tensor of multilinear ranks $…
M-theory compactified on -holonomy manifolds results in 4d supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained from a partially twisted 7d super Yang-Mills theory on a supersymmetric three-cycle…
The worldvolume theory of coincident M5-branes is expected to contain a nonabelian 2-form/nonabelian gerbe gauge theory that is a higher analog of self-dual Yang-Mills theory. But the precise details -- in particular the global moduli / instanton / magnetic charge structure -- have remained elusive. Here we deduce from…
Minimal 7D hypersurfaces degenerate under stability or bounded index constraints.
problem Degeneration of minimal hypersurfaces under stability or bounded index constraints.
method Analysis of sequences of minimal hypersurfaces, parameterization with controlled maps, and topological finiteness results.
result Minimal hypersurfaces can degenerate to singular ones with controlled geometry, topology, and singular set.
In 5D, integrability is linked to curvature constraints of subconformal structures.
problem Dispersionless integrability in 5D partial differential equations.
method Relating integrability to curvature constraints of subconformal structures.
result In 5D, integrability is characterized by the vanishing of a certain curvature of the subconformal structure.
Simulated annealing improves candidate optimization for multi-objective Bayesian optimization.
problem Efficient candidate optimization for multi-objective acquisition functions in Bayesian optimization.
method Simulated annealing-based approach for batch acquisition function optimization.
result Simulated annealing outperforms SLSQP in most multi-objective optimization problems, achieving higher hypervolume values and better convergence characteristics.