In this note we discuss conditions under which a linear connection on a manifold equipped with both a symmetric (Riemannian) and a skew-symmetric (almost-symplectic or Poisson) tensor field will preserve both structures. If (M, g) is a (pseudo-)Riemannian manifold, then classical results due to T. Levi-Civita, H. Weyl and E. Cartan [7] show that for any (1, 2) tensor field T i jk which is skew-...

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...

We consider the Mielke-Baekler model of three-dimensional AdS gravity with torsion, which has gravitational and translational Chern-Simons terms in addition to the usual Einstein-Hilbert action with cosmological constant. It is shown that the topological nature of the model leads to a finite Fefferman-Graham expansion. We derive the holographic stress tensor and the associated Ward identities a...

A generalization of the embedding approach for d-dimensional gravity based upon p-brane theories is considered. We show that the D-dimensional p-brane coupled to an antisymmetric tensor field of rank (p + 1) provides the dynamical basis for the description of d = (p + 1) dimensional gravity in the isometric embedding formalism. ”Physical” matter appears in such an approach as a manifestation of...

We study inflation driven by the Higgs field in Einstein-Cartan formulation of gravity. In this theory, presence Holst and Nieh-Yan terms with non-minimally coupled to them leads three additional coupling constants. For a broad range parameters, we find that is both possible consistent observations. most cases, spectral index given $n_s=1-2/N_\star$ (with $N_\star$ number e-foldings) whereas te...

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...

After a brief reminder of the Cartan 1-form and its application to the mechanics of point particles we review the application of Cartan 4-forms to eld theory.

We prove involutivity of Einstein and Einstein-Maxwell equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kähler theory are derived.

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...