Related papers: Generalized forms, vector fields and superspace
The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…
We introduce a new class of generalised quadratic forms over totally real number fields, which is rich enough to capture the arithmetic of arbitrary systems of quadrics over the rational numbers. We explore this connection through a version…
A rigorous formulation of Vessiot's vector field approach to the analysis of general systems of partial differential equations is provided. It is shown that this approach is equivalent to the formal theory of differential equations and that…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…
A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…
A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse…
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…
Recently proposed forms for gauge transformations with finite parameters in double field theory are discussed and problematic issues are identified. A new form for finite gauge transformations is derived that reveals the underlying gerbe…
This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full…
We establish certain fundamental properties of $f$-vectors and $F$-matrices for generalized cluster algebras, including the initial and final seed mutation formulas, the compatibility property and the symmetry property. Along the way, we…
The theory of contractions of multivectors, and star duality, was reorganized in a previous article, and here we present some applications. First, we study inner and outer spaces associated to a general multivector $M$ via the equations $v…
In this paper we use a generalized vector product to construct an exterior form $\wedge :(\mathbb{R}^{n}) ^{k}\to \mathbb{R}^{\binom{n}{k}}$, where $\binom{n}{k}=\frac{n!}{(n-k)!k!}$, $k\leq n$. Finally, for $n=k-1$ we introduce the…
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality…
Complete sets of bases of differential invariants, operators of invariant differentiation and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of…
Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…
The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry \`a la Hitchin). The generalized twistor space associated to such a manifold is…
We defined generalized \delta-derivations of algebra A as linear mapping \chi associated with usual \delta-derivation \phi by the rule \chi(xy)=\delta(\chi(x)y+x\phi(y))=\delta(\phi(x)y+x\chi(y)) for any x,y \in A. We described generalized…
Using families of curves to generalize vector fields, the Lie bracket is defined on a metric space, M. For M complete, versions of the local and global Frobenius theorems hold, and flows are shown to commute if and only if their bracket is…
This part of the series is devoted to the generalization of exterior differential calculus. I give definition to the integral of a five-vector form over a limited space-time volume of appropriate dimension; extend the notion of the exterior…
This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In a previous paper, we introduce the notion of formal manifolds and develop the…