A second-order differential identity for the Riemann tensor is obtained on a manifold with a symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors are derived from it. Applications to manifolds with recurrent or symmetric structures are discussed

recently, though particular cases were known for more than a century (e.g., any contact structure is “flat”: it can always be reduced, locally, to a canonical form). We give a general definition of the nonholonomic analogs of the Riemann and Weyl tensors. With the help of Premet’s theorems and a package

Here we continue to list the differential operators invariant with respect to the 15 exceptional simple Lie superalgebras g of polynomial vector fields. A part of the list (for operators acting on tensors with finite dimensional fibers) was earlier obtained in 2 of the 15 cases by Kochetkov

We study a model for quantum gravity on a circle in which the notion of a classical metric tensor is replaced by a quantum metric with an inhomogeneous transformation law under diffeomorphisms. This transformation law corresponds to the co–adjoint action of the Virasoro algebra, and resembles

Connections in fiber bundles, particularly in principal bundles, appear in many parts of differential geometry. For example, the basic invariant of a Riemannian metric—the Riemann curvature tensor—is the curvature of a canonical connection on the tangent bundle associated to the metric—the Levi

of diffusion processes on smooth manifolds. Thus we start by defining the invariant infinitesimal generators of diffusion processes of differential forms on smooth compact manifolds, in terms of the laplacians (on differential forms) associated with the Riemann-Cartan-Weyl (RCW) metric compatible connections

formulation of the RNS superstring. Key words: Beltrami differentials; deformations of covariant derivatives; stress tensor; con-formal invariance 2010 Mathematics Subject Classification: 32G05; 51M15; 51P05; 53Z05 1

This paper is intended to investigate the relation between electrodynamics in anisotropic material media and its analogous formulation in an spacetime, with non-null Riemann curvature tensor. After discussing the electromagnetism via chiral differential forms, we point out the optical activity of a

of structure tensors. Under ”generic ” assumptions the bifurcation problem reduces to an ODE which is invariant by an irreducible representation of the group of automorphisms G of the compact Riemann surface D/Γ. The irreducible representations of G have dimension one, two, three and four. The bifurcation

the Gromov-Witten invariants themselves. The moduli spaces of curves are endowed with tautological classes whose generating functions for their associated intersection numbers obey a system of differential equations which often possess remarkable properties [27, 17]. In this paper, we apply a mixture