Abstract: It is shown that the non-Archimedean field introduced by Levi-Civita [7, 8] admits a derivation and hence is a differential algebraic field [1, 2, 4]. The differential algebraic structure of the Levi-Civita field is utilized for the decision of differentiability of functional dependencies on a computer, as well as the practical computation of derivatives. As such, it represents a new ...

‎In this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎To this end‎, ‎we aim to replace the field of scalars $ mathbb{R} $ by self-adjoint elements of a commutative $ C^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎First‎, ‎we put forward the concept of operator-valued tensors and extend semi-Riemannian...

In this note, we discuss symmetric brackets on skew-symmetric algebroids associated with metric or symplectic structures. Given a pseudo-Riemannian structure, describe the induced by connections totally torsion in language of Lie derivatives and differentials functions. We formulate generalization fundamental theorem Riemannian geometry. particular, obtain an explicit formula Levi-Civita connec...

We consider the dynamics of three point masses, where we assume that the mass of the third body is so small that it does not affect the motion of the primaries. In the framework of the restricted three–body problem, we investigate the collisional trajectories, which correspond to a singularity of the equations of motion. We investigate the regularizing techniques known as Levi–Civita, Kustaanhe...

A geometry with parallel skew-symmetric torsion is a Riemannian manifold carrying metric connection torsion. Besides the trivial case of Levi-Civita connection, geometries non-vanishing arise naturally in several geometric contexts, e.g. on reductive homogeneous spaces, nearly Kähler or G2-manifolds, Sasakian and 3-Sasakian manifolds, twistor spaces over quaternion-Kähler manifolds positive sca...

We define a Lévy process on smooth manifold M with connection as projection of solution Marcus stochastic differential equation holonomy bundle M, driven by holonomy-invariant Euclidean space. On Riemannian manifold, our definition (with Levi-Civita connection) generalizes the Eells-Elworthy-Malliavin construction Brownian motion and extends class isotropic introduced in Applebaum Estrade [3]. ...

In the general framework of Metric-Affine theories gravity, where metric and connection are independent variables, we consider actions quadratic in Ricci scalar curvature Holst invariant (the contraction Riemann with Levi-Civita antisymmetric tensor) coupled non-minimally to a field. We study profile equivalent effective theory, featuring an extra dynamical pseudoscalar degree freedom, show tha...

a cartan manifold is a smooth manifold m whose slit cotangent bundle 0t *m is endowed with a regularhamiltonian k which is positively homogeneous of degree 2 in momenta. the hamiltonian k defines a (pseudo)-riemannian metric ij g in the vertical bundle over 0 t *m and using it, a sasaki type metric on 0 t *m is constructed. a natural almost complex structure is also defined by k on 0 t *m in su...

For a compact Lie group G we consider lattice gauge model given by the G-Hamiltonian system which consists of cotangent bundle power with its canonical symplectic structure and standard moment map. We explicitly construct Fedosov quantization underlying manifold using Levi–Civita connection Killing metric on G. then explain refine quantized homological reduction for construction star product sy...