Related papers: Constructing Ricci vector fields on $\mathbb R^2$ …
We introduce a particular family of two-dimensional surfaces in $\mathbb R^4$ which generalize the classical Dini surfaces in $\mathbb R^3$.
The article considers some concrete solutions to the Dirac equation coupled to a vector bundle with connection, arising in the study of Yang-Mills equations and vector bundles on Riemann surfaces.
There are described equations for a pair comprising a Riemannian metric and a Killing field on a surface that contain as special cases the Einstein Weyl equations (in the sense of D. Calderbank) and a real version of a special case of the…
Research on spatially-structured light has seen an explosion in activity over the past decades, powered by technological advances for generating such light, and driven by questions of fundamental science as well as engineering applications.…
We study the geometry at infinity of expanding gradient Ricci solitons of dimension greater than two with finite asymptotic curvature ratio without curvature sign assumptions. We mainly prove that they have a cone structure at infinity.
We demonstrate how to find both the color diagonal form of the squared Dirac equation in the axial color background and the transformation of the color space, which makes this equation diagonal.
The problem of defining correctly geometric objects such as the curvature is a hard one in discrete geometry. In 2009, Ollivier defined a notion of curvature applicable to a wide category of measured metric spaces, in particular to graphs.…
We construct a polynomial planar vector field of degree two with one invariant algebraic curves of large degree. We exhibit an explicit quadratic vector fields which invariant curves of degree nine, twelve, fifteen and eighteen degree.
We develop techniques for solving the relative isoperimetric problem on polygonal domains in $\mathbb{R}^2$, with special attention paid to corners. As an application, we solve the relative isoperimetric problem for a square with a square…
Ricci flow on two dimensional surfaces is far simpler than in the higher dimensional cases. This presents an opportunity to obtain much more detailed and comprehensive results. We review the basic facts about this flow, including the…
We prove the equivalence between the several notions of generalized Ricci curvature found in the literature. As an application, we characterize when the total generalized Ricci tensor is symmetric.
The aim of the present paper is to investigate intrinsically the notion of a concircular $\pi$-vector field in Finsler geometry. This generalizes the concept of a concircular vector field in Riemannian geometry and the concept of a…
We give characterizations of affine transformations and affine vector fields in terms of the spray. By utilizing the Jacobi type equation that characterizes affine vector fields, we prove some rigidity theorems of affine vector fields on…
We investigate the properties of the combinatorial Ricci flow for surfaces, both forward and backward -- existence, uniqueness and singularities formation. We show that the positive results that exist for the smooth Ricci flow also hold for…
We define the Ricci curvature, as a measure, for certain singular torsion-free connections on the tangent bundle of a manifold. The definition uses an integral formula and vector-valued half-densities. We give relevant examples in which the…
The purpose of the present article is to study and characterize sev- eral types of symmetries of generalized Robertson-Walker space-times. Con- formal vector fields, curvature and Ricci collineations are studied. Many im- plications for…
We completely describe paracontact metric three-manifolds whose Reeb vector field satisfies the Ricci soliton equation. While contact Riemannian (or Lorentz\-ian) Ricci solitons are necessarily trivial, that is, $K$-contact and Einstein,…
The aim of this paper is to present a direct and simple proof of a result concerning the existence of metrics of positive Ricci curvature on the total space of fiber bundles with compact structure groups. In particular, it also generalizes…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
In this thesis, we study connections between metric and combinatorial graphs from a Dirichlet space point of view.