We build an analogue for the Levi-Civita connection on Riemannian manifolds for sub-Riemannian manfiolds modeled on the Heisenberg group. We demonstrate some geometric properties of this connection to justify our choice and show that this connection is unique in having these properties.

The object of the present paper is to study locally φsymmetric LP-Sasakian manifolds admitting semi-symmetric metric connection and obtain a necessary and sufficient condition for a locally φsymmetric LP-Sasakian manifold with respect to semi-symmetric metric connection to be locally φ-symmetric LP-Sasakian manifold with respect to Levi-Civita connection. AMS Mathematics Subject Classification ...

We develop a new model of a spinning particle in Brans-Dicke space-time using a metric-compatible connection with torsion. The particle's spin vector is shown to be Fermi-parallel (by the Levi-Civita connection) along its worldline (an autoparallel of the metric-compatible connection) when neglecting spin-curvature coupling.

We show that a 7-dimensional non-compact Ricci-flat Riemannian manifold with Riemannian holonomy G2 can admit non-integrable G2 structures of type R⊕S 2 0 (R )⊕R in the sense of Fernández and Gray. This relies on the construction of some G2 solvmanifolds, whose Levi-Civita connection is known to give a parallel spinor, admitting a 2-parameter family of metric connections with non-zero skew-symm...

The geometric constructions are performed on (semi) Riemannian manifolds and vector bundles provided with nonintegrable distributions defining nonlinear connection structures induced canonically by metric tensors. Such spaces are called nonholonomic manifolds and described by two equivalent linear connections also induced unique forms by a metric tensor (the Levi Civita and the canonical distin...

We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikeš, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively invariant finite-type linear system of partial differential equations. Prolonging this system, we may reformulate these equations as defining covariant constant sec...

Finsler and Lagrange spaces can be equivalently represented as almost Kähler manifolds endowed with a metric compatible canonical distinguished connection structure generalizing the Levi Civita connection. The goal of this paper is to perform a natural Fedosov– type deformation quantization of such geometries. All constructions are canonically derived for regular Lagrangians and/or fundamental ...

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...

We prove the existence and uniqueness of Levi-Civita connections for strongly [Formula: see text]-compatible pseudo-Riemannian metrics on tame differential calculi. Such properly contain classes bilinear as well their conformal deformations. This extends previous results in [J. Bhowmick, D. Goswami S. Mukhopadhyay, a class spectral triples, Lett. Math. Phys. 110 (2020) 835–884] G. Landi, On Kos...

We study lightlike hypersurfaces of a semi-Riemannian product manifold. We introduce a class of lightlike hypersurfaces called screen semi-invariant lightlike hypersurfaces and radical antiinvariant lightlike hypersurfaces. We consider lightlike hypersurfaces with respect to a quartersymmetric nonmetric connection which is determined by the product structure. We give some equivalent conditions ...