New perspective on G2-structures flow from DeTurck Laplacian.
problem Understanding G2-structures and their flows.
method Introducing a new flow (DeTurck Laplacian flow) for G2-structures.
result DeTurck Laplacian flow is a flow of G2-structures.
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9 results for “G2-geometry”
We prove a general result about the stability of geometric flows of "closed" sections of vector bundles on compact manifolds. Our theorem allows to prove a stability result for the modified Laplacian coflow in G2-geometry introduced by Grigorian and for the balanced flow introduced by the authors in a previous paper.
The concept of soliton, in its most general version, allows us to find canonical or distinguished elements on any set provided with an equivalence relation and an `optimal' tangent direction at each point. We study in this paper solitons on homogeneous spaces, which have consolidated its role as a quite useful tool to …
In G2 manifolds, 3-dimensional associative submanifolds (instantons) play a role similar to J-holomorphic curves in symplectic geometry. In [21], instantons in G2 manifolds were constructed from regular J-holomorphic curves in coassociative submanifolds. In this exposition paper, after reviewing the background of G2 ge…
New geometric flow called hypersymplectic flow studied, proving key properties.
problem Understanding and proving properties of hypersymplectic flow.
method Explained original ideas, surveyed progress, proved new results.
result Proved complete torsion-free hypersymplectic structure must be hyperkähler.
The -dimensional link of a weighted homogeneous hypersurface on the round -sphere in has a nontrivial null Sasakian structure which is contact Calabi-Yau, in many cases. It admits a canonical co-closed -structure induced by the Calabi-Yau -orbifold basic geometry. We disti…
Aerobatics of flying saucersmath.DG
Starting from the observation that a flying saucer is a nonholonomic mechanical system whose 5-dimensional configuration space is a contact manifold, we show how to enrich this space with a number of geometric structures by imposing further nonlinear restrictions on the saucer's velocity. These restrictions define cert…
We study the Hitchin component in the space of representations of the fundamental group of a Riemann surface into a split real simple Lie group in the rank 2 case. We prove that such representations are described by a conformal structure and class of Higgs bundle we call cyclic and we show cyclic Higgs bundles correspo…
Extends Coulomb gauge existence to non-associative gauge theory.
problem Existence of configurations with divergence-free torsion in non-associative gauge theory.
method Analyzes non-associative gauge theory based on smooth loops and their tangent algebras, proving existence of configurations with divergence-free torsion.
result Proves existence of configurations with divergence-free torsion given a sufficiently small torsion in a Sobolev norm.