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Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
We establish a 1-to-1 relation between metrics on compact Riemann surfaces without boundary, and mechanical systems having those surfaces as configuration spaces.
This article explores the Conformal Ricci Collineations (CRCs) for the plane-symmetric static spacetime. The non-linear coupled CRC equations are solved to get the general form of conformal Ricci symmetries. In the non-degenerate case, it…
The Euler-Lagrange equations for some class of gravitational actions are calculated by means of Palatini principle. Polynomial structures with Einstein metrics appear among extremals of this variational problem.
Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…
We consider nonhomogeneous fractional $p$-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish…
We construct examples of Bach-flat gradient Ricci solitons which are neither half conformally flat nor conformally Einstein.
We study several classes of Riemannian manifolds which are defined by imposing a certain condition on the Ricci tensor. We consider the following cases: Ricci recurrent, Cotton, quasi Einstein and pseudo Ricci symmetric condition. Such…
The pullback approach to global Finsler geometry is adopted. Some new types of special Finsler spaces are introduced and investigated, namely, Ricci, generalized Ricci, projectively recurrent and m-projectively recurrent Finsler spaces. The…
Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit…
Given a finite connected bipartite graph, finite-dimensional indecomposable semisimple Leibniz algebras are constructed. Furthermore, any finite-dimensional indecomposable semisimple Leibniz algebra admits a similar construction.
The set of matrix tuples with invariant subspaces whose dimensions sum up to the dimension of the space, but which do not span the whole space form an algebraic hypersurface. We found the equation of this hypersurface. This generalizes…
In this short note we provide several conjectures on the regularity of measured Gromov-Hausdorff limit spaces of Riemannian manifolds with Ricci curvature bounded below, from the point of view of the synthetic treatment of lower bounds on…
We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional…
This article is an overview of the results obtained in recent years on symplectic connections. We present what is known about preferred connections (critical points of a variational principle). The class of Ricci-type connections (for which…
Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split…
We present a characterization of $2$-dimensional Lorentzian manifolds with constant Ricci scalar curvature. It is well known that every $2$-dimensional Lorentzian manifolds is conformally flat, so we rewrite the Ricci scalar curvature in…
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for…