arXiv subjects

Georgi Dzhelepov

Publications and source records attributed to Georgi Dzhelepov.

6 recordsLinked to original sources

arXiv2023

Spheres and circles with respect to an indefinite metric on a Riemanian manifold with a skew-circulant structure

We study hyper-spheres, spheres and circles, with respect to an indefinite metric, in a tangent space on a 4-dimensional differentiable manifold. The manifold is equipped with a positive definite metric and an additional tensor structure of type (1, 1)11. The fourth power of the additional structure is minus identity and its components form a skew-circulant matrix in some local coordinate system. The both structures are compatible and they determine an associated indefinite metric on the manifold.

math.DG↗

arXiv2020

The value of the work done by an isotropic vector force field along an isotropic curve

In the present paper we consider a 3-dimensional differentiable manifold $M$ equipped with a Riemannian metric $g$ and an endomorphism $Q$, whose third power is the identity and $Q$ acts as an isometry on $g$. Both structures $g$ and $Q$ determine an associated metric $f$ on $(M, g, Q)$. The metric $f$ is necessary indefinite and it defines isotropic vectors in the tangent space $T_{p}M$ at an arbitrary point $p$ on $M$. The physical forces are represented by vector fields. We investigate physical forces whose vectors are in $T_{p}M$ on $(M, g, Q)$. Moreover, these vectors are isotropic and they act along isotropic curves. We study the physical work done by such forces.

math.DG↗

arXiv2017

Three-dimensional Riemannian manifolds with circulant structures

We consider a 3-dimensional Riemannian manifold M with two circulant structures -- a metric g and an endomorphism q whose third power is identity. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We obtain some curvature properties of this manifold (M, g, q) and give an explicit example of such a manifold.

math.DG↗

arXiv2017

On a Three Dimensional Riemannian Manifold with an Additional Structure

We consider a 3-dimensional Riemannian manifold with additional structure q. We find a condition that the affine structure q is parallel with respect to the Riamannian connection.We prove the sectional curvatures of three 2-sections formed linearly independent vectors are equal among them.

math.DG↗

arXiv2017

Spheres and circles with respect to an indefinite metric on a Riemannian manifold with circulant structures

We consider a $3$-dimensional differentiable manifold with two circulant structures -- a Riemannian metric and an additional structure, whose third power is the identity. The structure is compatible with the metric such that an isometry is induced in any tangent space of the manifold. Further, we consider an associated metric with the Riemannian metric, which is necessary indefinite. We find equations of a sphere and of a circle, which are given in terms of the associated metric, with respect to the Riemannian metric.

math.DG↗

arXiv2010

Almost conformal transformation in a class of Riemannian manifolds

We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we construct an infinite series of circulant metrics which are successively almost conformaly related. In this case we get some properties.

math.DG↗