Related papers: Upon h-normal \Gamma-linear connections on J^1(T,M…
The paper introduces the notion of \Gamma-linear connection \nabla on the 1-jet fibre bundle J^1(T,M), and presents its local components. We also describe the local Ricci and Bianchi identities of $\nabla$.
In this paper we describe the local Ricci and Bianchi identities for an h-normal N-linear connection D\Gamma(N) on the dual 1-jet space J^{1*}(T,M). To reach this aim, we firstly give the expressions of the local distinguished (d-) adapted…
The aim of this paper is to describe the local Bianchi identities for an $h$-normal $\Gamma$-linear connection of Cartan type $\nabla\Gamma$ on the first-order jet space $J^1(R,M)$. In this direction, we present the local expressions of the…
The aim of this paper is to present the main geometrical objects on the dual 1-jet bundle $J^{1*}(\cal{T},M)$ (this is the polymomentum phase space of the De Donder-Weyl covariant Hamiltonian formulation of field theory) that characterize…
This paper introduces $\anabla$-tensors on lightlike hypersurfaces $M^{n+1}$ of signature $(0,n)$, $(n\geq 1)$ and investigates on their properties in connection with the null geometry of $M$. In particular, we show that there is an…
Let $P(M,G)$ be a principal fiber bundle, let $\omega$ be a connection form on $P(M,G)$, and consider a projectable connection $\nabla^{P}$ on $P(M,G)$. The aim of this work is to determine the $\nabla^{P}$-martingales in $P(M,G)$. Our…
The aim of this paper is to study the local components of the relativistic time dependent d-linear connections, d-torsions, d-curvatures and deflection d-tensors with respect to an adapted basis on the 1-jet space $J^{1}(R,M)$. The Ricci…
In this paper, we investigate the geometry of the tangent bundle $TM$ of a statistical manifold $(M,g,\nabla)$ endowed with a two-parameter family of generalized Cheeger--Gromoll metrics $g_{p,q}$. We compute the associated the Levi--Civita…
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…
Given a manifold M with a submanifold N, the deformation space D(M,N) is a manifold with a submersion to R whose zero fiber is the normal bundle, and all other fibers are equal to M. This article uses deformation spaces to study the local…
Let $M$ be an $n-$dimensional differentiable manifold with a symmetric connection $\nabla $ and $T^{\ast}M$ be its cotangent bundle. In this paper, we study some properties of the modified Riemannian extension $% \widetilde{g}_{\nabla,c}$…
Following the approach of Budzy\'nski and Kondracki, we define covariant differential algebras and connections on locally trivial quantum principal fibre bundles. We also consider covariant derivatives, connection forms and curvatures and…
The direct string computation of anomalous D-brane and orientifold plane couplings is extended to include the curvature of the normal bundle. The normalization of these terms is fixed unambiguously. New, non-anomalous gravitational…
This paper presents a brief study on connections on fiber, principal and vector smooth bundles as well as some relations with their curvatures.
The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic…
We give coordinate formula and geometric description of the curvature of the tensor product connection of linear connections on vector bundles with the same base manifold. We define the covariant differential of geometric fields of certain…
We consider a family of $\alpha$-connections defined by a pair of generalized dual quasi-statistical connections $(\hat{\nabla},\hat{\nabla}^*)$ on the generalized tangent bundle $(TM\oplus T^*M, \check{h})$ and determine their curvature,…
The paper developes a geometrization of a Kronecker $h$-regular vertical fundamental metrical d-tensor $G^{(\alpha)(\beta)}_{(i)(j)}$ on the jet fibre bundle of order one $J^1(T,M)$. This geometrization gives a mathematical model for both…
Given a real, finite-dimensional, smooth parallelizable Riemannian manifold $(\mathcal{N},G)$ endowed with a teleparallel connection $\nabla$ determined by a choice of a global basis of vector fields on $\mathcal{N}$, we show that the…
In a fibre bundle, natural derivatives of a section are defined as tangent vector fields on the image of a section of the fibre bundle. A local extension to vector fields in the tangent bundle leads to a direct proof of the formula…