Deformations of levi flat structures in smooth manifolds
TLDR
In this paper, the intrinsic deformations of Levi flat structures on a smooth manifold were studied, and a complex whose cohomology group of order 1 contains the infinitesimal deformation of a Levi flat structure was defined.Abstract:
We study intrinsic deformations of Levi flat structures on a smooth manifold. A Levi flat structure on a smooth manifold L is a couple (ξ, J) where ξ ⊂ T(L) is an integrable distribution of codimension 1 and J : ξ → ξ is a bundle automorphism which defines a complex integrable structure on each leaf. A deformation of a Levi flat structure (ξ, J) is a smooth family {(ξt, Jt)}t∈]-e,e[ of Levi flat structures on L such that (ξ0, J0) = (ξ, J). We define a complex whose cohomology group of order 1 contains the infinitesimal deformations of a Levi flat structure. In the case of real analytic Levi flat structures, this cohomology group is where (𝒵*(L), δ, {⋅,⋅}) is the differential graded Lie algebra associated to ξ.read more
Citations
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Book
Complex manifolds and deformation of complex structures
TL;DR: In this paper, the existence of Weak Solutions of a Strongly Elliptic Partial Differential Equation (SLEE) was shown to be a regularity of weak solutions of EDEs.
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On the Obstruction of the Deformation Theory in the DGLA of Graded Derivations
TL;DR: In this paper, it was shown that the deformation theory in the DGLA of graded derivations is not obstructed, but it is level-wise obstructed by the Frolicher-Nijenhuis bracket.
References
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Deformation Quantization of Poisson Manifolds
TL;DR: In this paper, it was shown that every finite-dimensional Poisson manifold X admits a canonical deformation quantization, and that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one correspondence with the class of Poisson structures on X modulo diffeomorphisms.
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Deformation quantization of Poisson manifolds, I
TL;DR: In this paper, it was shown that every finite-dimensional Poisson manifold X admits a canonical deformation quantization, which can be interpreted as correlators in topological open string theory.
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On the Deformation of Rings and Algebras
TL;DR: In this article, the deformation theory for algebras is studied in terms of the set of structure constants as a parameter space, and an example justifying the choice of parameter space is given.
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The deformation theory of representations of fundamental groups of compact Kähler manifolds
TL;DR: In this article, it was shown that there exists a neighborhood of ρ in ℜ(Γ, G) which is analytically equivalent to a cone defined by homogeneous quadratic equations.
Journal ArticleDOI
Cohomology and deformations in graded lie algebras
TL;DR: In this paper, it was shown that deformability is to a large extent determined by certain cohomology groups and mappings of these, and that the deformability of a single element x of degree one in a graded Lie algebra subject to the condition (x,x) = 0 is determined by the structure of these cohomologies.