The hypersymplectic deformation conjecture asserts that a hypersymplectic structure given by a triple on a closed connected oriented smooth four-manifold
can be smoothly deformed, within the cohomology class
of each form, to a hyper-Kähler triple. For a normalized initial triple satisfying
,
the final triple is required to satisfy 
for a common positive volume form 
.
Hypersymplectic Deformation Conjecture
See also
Cohomology Class, Hyper-Kähler Manifold, Hypersymplectic Structure, K3 SurfaceExplore with Wolfram|Alpha
References
Fine, J. and Yao, C. "Hypersymplectic 4-Manifolds, the
-Laplacian Flow and Extension Assuming Bounded Scalar Curvature."
Duke Math. J. 167, 3533-3589, 2018. https://doi.org/10.1215/00127094-2018-0040.
Cite this as:
Weisstein, Eric W. "Hypersymplectic Deformation Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HypersymplecticDeformationConjecture.html