English
norskBlar i forfatter "Schneider, Eivind"
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Decomposable (5, 6)-solutions in eleven-dimensional supergravity
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023-06-08)We present decomposable (5, 6)-solutions M<sup>1,4</sup>×M<sup>6</sup> in eleven-dimensional supergravity by solving the bosonic supergravity equations for a variety of non-trivial flux forms. Many of the bosonic backgrounds presented here are induced by various types of null flux forms on products of certain totally Ricci-isotropic Lorentzian Walker manifolds and Ricci-flat Riemannian manifolds. ... -
Differential invariants of Einstein-Weyl structures in 3D
(Journal article; Tidsskriftartikkel; Peer reviewed, 2018-05-22)Einstein–Weyl structures on a three-dimensional manifold <i>M</i> are given by a system <i>E</i> of PDEs on sections of a bundle over <i>M</i>. This system is invariant under the Lie pseudogroup <i>G</i> of local diffeomorphisms on <i>M</i>. Two Einstein–Weyl structures are locally equivalent if there exists a local diffeomorphism taking one to the other. Our goal is to describe the quotient equation ... -
Differential invariants of Kundt spacetimes
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-09-07)We find generators for the algebra of rational differential invariants for general and degenerate Kundt spacetimes and relate this to other approaches to the equivalence problem for Lorentzian metrics. Special attention is given to dimensions three and four. -
Differential invariants of Kundt waves
(Journal article; Tidsskriftartikkel; Peer reviewed, 2019-07-17)Kundt waves belong to the class of spacetimes which are not distinguished by their scalar curvature invariants. We address the equivalence problem for the metrics in this class via scalar differential invariants with respect to the equivalence pseudo-group of the problem. We compute and finitely represent the algebra of those on the generic stratum and also specify the behavior for vacuum Kundt ... -
Differential invariants of Lie pseudogroups
(Doctoral thesis; Doktorgradsavhandling, 2019-05-10)We compute differential invariants for several Lie pseudogroups, and use them for solving the equivalence and classification problem for a variety of mathematical structures appearing in geometry and mathematical physics. We demonstrate utility of the algebra of rational scalar differential invariants for solving these two problems, also in cases where the structures are given as solutions to a ... -
Differential invariants of self-dual conformal structures
(Journal article; Tidsskriftartikkel; Peer reviewed, 2016-06-17)We compute the quotient of the self-duality equation for conformal metrics by the action of the diffeomorphism group. We also determine Hilbert polynomial, counting the number of independent scalar differential invariants depending on the jet-order, and the corresponding Poincaré function. We describe the field of rational differential invariants separating generic orbits of the diffeomorphism ... -
ODEs whose Symmetry Groups are not Fiber-Preserving
(Journal article; Tidsskriftartikkel; Peer reviewed, 2023)We observe that, up to conjugation, a majority of higher order ODEs (ordinary differential equations) and ODE systems have only fiber-preserving point symmetries. By exploiting Lie's classification of Lie algebras of vector fields, we describe all exceptions to this in the case of scalar ODEs and systems of ODEs on a pair of functions. The scalar ODEs whose symmetry algebras are not fiber preserving ... -
Projectable Lie algebras of vector fields in 3D
(Journal article; Tidsskriftartikkel; Peer reviewed, 2018-06-15)Starting with Lie’s classification of finite-dimensional transitive Lie algebras of vector fields on <b>C<sup>2</sup></b> we construct transitive Lie algebras of vector fields on the bundle <b>C<sup>2</sup> x C</b> by lifting the Lie algebras from the base. There are essentially three types of transitive lifts and we compute all of them for the Lie algebras from Lie’s classification. The simplest ... -
Symmetry transformation groups and differential invariants
(Master thesis; Mastergradsoppgave, 2014-11-15)There exists a local classification of finite-dimensional Lie algebras of vector fields in two complex dimensions. We lift the Lie algebras from this classification to three complex dimensions.
