arXiv subjects

Miroslav Maksimović

Publications and source records attributed to Miroslav Maksimović.

5 recordsLinked to original sources

arXiv2026

Einstein connection of a weak almost contact metric manifold

Advances in modern physics since Einstein have made the nonsymmetric metric (0,2)-tensor $G=g+F$, where $g$ is a pseudo-Riemannian metric associated with gravity, and $F\ne0$ is a skew-symmetric tensor associated with electromagnetism, more attractive than ever. Einstein considered a linear connection $\nabla$ with torsion $T$ such that $(\nabla_X\,G)(Y,Z)=G(T(Y,X),Z)$. In this paper, we explicitly present the Einstein connection of $G=g+F$ using a weak almost contact structure $(f,ξ,η)$ with $g(X,fY)=F(X,Y)$ with a natural condition (trivial in the almost contact case). We discuss special Einstein connections, and give an example in terms of the weighted product of almost Hermitian manifold and a real line.

math.DG↗

arXiv2026

A semi-symmetric metric connection, perfect fluid space-time and phantom barrier

We consider a concircularly semi-symmetric metric connection and its application. The Ricci tensors with respect to the concircularly semi-symmetric metric connection are symmetric, and they are used to define Einstein type manifolds. In this way, conditions under which a pseudo-Riemannian manifold is quasi-Einstein are obtained. On a Lorentzian manifold, a concircularly semi-symmetric metric connection with a unit timelike generator becomes a semi-symmetric metric $P$-connection, and a Lorentzian manifold becomes a GRW space-time. { It is proven in which case the scalar curvature of a perfect fluid space-time with that connection is constant and what its value is, which implies a reduction to Einstein manifold. } Furthermore, an application to the theory of relativity is presented, and the value of the equation of state is examined. It is ultimately shown that the equation of state in a perfect fluid space-time that satisfies Einstein field equation with cosmological constant and admits a unit timelike torse-forming vector represents a phantom barrier.

math.DG↗

arXiv2026

Canonical parameters on marginally trapped surfaces in the Minkowski 4-space

Marginally trapped surfaces are spacelike surfaces in the Minkowski space whose mean curvature vector is lightlike at each point. In general, the marginally trapped surfaces are determined by seven functions satisfying several conditions (differential equations). In the present paper, we introduce special principal parameters, called canonical, and prove that every marginally trapped surface of general type admits (at least locally) canonical principal parameters which allow us to reduce the number functions. We prove a Fundamental existence and uniqueness theorem formulated in terms of canonical parameters, which states that every marginally trapped surface is determined up to a motion by three smooth functions satisfying a system of partial differential equations.

math.DG↗

arXiv2024

Quarter-symmetric non-metric connection

The paper will study a new quarter-symmetric non-metric connection on a generalized Riemannian manifold. It will determine the relations that the torsion tensor satisfies. The exterior derivative of the skew-symmetric part $F$ of basic tensor $G$ with respect to the Levi-Civita connection coincides with that of skew-symmetric part $F$ with respect to quarter-symmetric non-metric connection, which implies that the even-dimensional manifold endowed with $F$ is symplectic manifold if and only if it is closed with respect to quarter-symmetric non-metric connection. The linearly independent curvature tensors of this connection and its dual connection are determined and the properties of these tensors are discussed. Finally, the condition is given that the connection should be dual symmetric.

math.DG↗

arXiv2023

Quarter-symmetric connection on an almost Hermitian manifold and on a Kähler manifold

The paper observes an almost Hermitian manifold as an example of a generalized Riemannian manifold and examines the application of a quarter-symmetric connection on the almost Hermitian manifold. The almost Hermitian manifold with quarter-symmetric connection preserving the generalized Riemannian metric is actually the Kähler manifold. Observing the six linearly independent curvature tensors with respect to the quarter-symmetric connection, we construct tensors that do not depend on the quarter-symmetric connection generator. One of them coincides with the Weyl projective curvature tensor of symmetric metric $g$. Also, we obtain the relations between the Weyl projective curvature tensor and the holomorphically projective curvature tensor. Moreover, we examine the properties of curvature tensors when some tensors are hybrid.

math.DG↗