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.

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 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.

In this paper, we present the classification of 2 and 3-dimensional Calabi hypersurfaces with parallel Fubini-Pick form respect to Levi-Civita connection metric.

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 ...

Let M be a differentiable manifold. We say that a tensor field g defined on M is non-regular if g is in some local L space or if g is continuous. In this work we define a mollifier smoothing gε of g that has the following feature: If g is a Riemannian metric of class C, then the Levi-Civita connection and the Riemannian curvature tensor of gε converges to the Levi-Civita connection and to the R...

In this paper we introduce the Cheeger-Gromoll type metric on coframe bundle of a Riemannian manifold and investigate Levi-Civita connection, curvature tensor, sectional geodesics with metric.

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...