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Displaying similar documents to “Forms equivalent to curvatures.”

Connections with prescribed curvature

Dennis Deturck, Janet Talvacchia (1987)

Annales de l'institut Fourier

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We discuss the problem of prescribing the curvature of a connection on a principal bundle whose base manifold is three-dimensional. In particular, we consider the local question: Given a curvature form F , when does there exist locally a connection A such that F is the curvature of A  ? When the structure group of the bundle is semisimple, a finite number of nonlinear identities arise as necessary conditions for local solvability of the curvature equation. We conjecture that these conditions...

Decomposition in the large of two-forms of constant rank

Ibrahim Dibag (1974)

Annales de l'institut Fourier

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The purpose of this paper is to find necessary and sufficient conditions for globally-decomposing an exterior 2-form w , of constant rank 2 s , on a vector-bundle E , as a sum : w = y 1 ∧ y s + 1 + ⋯ + y s ∧ y 2 s . The general theory is applied to low dimensional manifolds, spheres, real and complex projective spaces.

Geometry of isotypic Kronecker webs

Wojciech Kryński (2012)

Open Mathematics

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An isotypic Kronecker web is a family of corank m foliations { ℱ t } t ∈ ℝ P 1 such that the curve of annihilators t ↦ (T x F t)⊥ ∈ Grm(T x* M) is a rational normal curve in the Grassmannian Grm(T x*M) at any point x ∈ M. For m = 1 we get Veronese webs introduced by I. Gelfand and I. Zakharevich [Gelfand I.M., Zakharevich I., Webs, Veronese curves, and bi-Hamiltonian systems, J. Funct. Anal., 1991, 99(1), 150–178]. In the present paper, we consider the problem of local classification of isotypic Kronecker...