arXiv research

Study develops a cost model for field canals improvement projects in Egypt.

The paper studies canal hypersurfaces in Lorentz-Minkowski 4-space.

The study characterizes canal hypersurfaces formed by non-null curves with parallel frame in Minkowski space-time.

The paper studies canal hypersurfaces in Lorentz-Minkowski 4-space.

The study characterizes canal hypersurfaces in Euclidean spaces and their curvature properties.

The geometry of canal hypersurfaces of an n-dimensional conformal space C^n is studied. Such hypersurfaces are envelopes of r-parameter families of hyperspheres, 1 \leq r \leq n-2. In the present paper the conditions that characterize canal hypersurfaces, and which were known earlier, are made more precise. The main at…

A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t). In this paper, we investigate when parameter curves of the canal surface are also lines of curvature. Last of all, for special spine curves we obtain the radius …

In this study, we consider canal surfaces according to parallel transport frame in Euclidean space $\mathbb{E}^{4}$. The curvature properties of these surfaces are investigated with respect to $k_{1}$, $k_{2}$ and $k_{3}$ which are principal curvature functions according to parallel transport frame. We also give an exa…

In this paper, we obtain the differential equations of the space-like loxodromes on the non-degenerate canal surfaces depending on the causal characters of these canal surfaces and their meridians in Minkowski 3-space. Also we give an example by using Mathematica computer programme.

In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R^3. By means of a connection of the differential equations for these curvature lines and real Ricc…

In this study, we analyze the general canal surfaces in terms of the features flat, II-flat minimality and II-minimality, namely we study under which conditions the first and second Gauss and mean curvature vanishes, i.e. K=0, H=0, K_{II}=0 and H_{II} =0. We give a non-existence result for general canal surfaces in E^3…

The paper explores $K^α$-translators on parallel and canal surfaces in 3D space.

In this study, we investigated the (K,H), (K,K_{II}), (H,K_{II})-Weingarten and (K,H),(K,K_{II}),(H,K_{II}) and (K,H,K_{II})-linear Weingarten canal surfaces in IR^3.

New surface class defined using osculating circles.

We find the minimal value of the length in de Sitter space of closed space-like curves with non-vanishing non-space-like geodesic curvature vector. These curves are in correspondence with closed almost-regular canal surfaces, and their length is a natural magnitude in conformal geometry. As an application, we get a low…

Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal sectional curvatures are locally equivalent to canal hypersurfaces in Euclidean spa…

Isophote comprises a locus of the surface points whose normal vectors make a constant angle with a fixed vector. Main objective of this paper is to find the axis of an isophote curve via its Darboux frame and afterwards to give some characterizations about isophote and its axis. Particularly, for isophotes lying on a c…

A space curve is determined by conformal arc-length, conformal curvature, and conformal torsion, up to Möbius transformations. We use the spaces of osculating circles and spheres to give a conformally defined moving frame of a curve in the Minkowski space, which can naturally produce the conformal invariants and the no…

The width of a closed convex subset of Euclidean space is the distance between two parallel supporting planes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n > 2. In this paper we describe a necessary condition that th…

In this paper, we show that a generalized Sasakian space form of dimension greater than three is either of constant sectional curvature; or a canal hypersurface in Euclidean or Minkowski spaces; or locally a certain type of twisted product of a real line and a flat almost Hermitian manifold; or locally a wapred product…

Study loxodromes and geodesics on rotational surfaces in pseudo-isotropic space.

Multinational corporations use highly complex structures of parents and subsidiaries to organize their operations and ownership. Offshore Financial Centers (OFCs) facilitate these structures through low taxation and lenient regulation, but are increasingly under scrutiny, for instance for enabling tax avoidance. Theref…

Characterizes winding of braided vector fields in tubular domains.

Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.

The paper explores how fields in higher dimensions are quantized.

Paper transforms torse-forming vector fields into simpler forms.

Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.

Every smooth vector field is a combination of gradient fields.

Conformal vector fields on LCP manifolds are orthogonal and Killing.

Paper describes holomorphic polyvector fields on toric varieties.

Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.

The paper proves that certain modified conformal vector fields are trivial on compact and non-compact manifolds.

We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. In particular, in the case of admissible regular sheaves of local fields defined on a simply connected manifold, we obtain a global extension result for every local field of the sheaf. This generalizes…

The paper establishes a connection between force-free fields and conformally geodesic fields.

Unified physics field theories through a general conservation law.

We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz e…

Vector fields invariant under Lie group action are finitely generated by polynomial fields.

Quantum field theory uses Lorentzian bordisms to describe time evolution.

The position vector field x is the most elementary and natural geometric object on a Euclidean submanifold $M$. The position vector field plays very important roles in mathematics as well as in physics. Similarly, the tangential component x^T of the position vector field is the most natural vector field tangent to the …

Study on vector fields on Lie groups reveals surprising algebraic coincidences.

This work discovers latent field effects governing interacting dynamical systems.

Study proves conformal vector fields on certain Finsler manifolds are Killing fields.

For a submanifold M in a Euclidean space, the tangential component x^T of the position vector field x of M is the most natural vector field tangent to the Euclidean submanifold, called the canonical vector field of M. In this article, first we prove that the canonical vector field of every Euclidean submanifold is alwa…

Study magnetic field evolution in inhomogeneous axion stars.

Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.

A Ricci soliton $(M,g,v,λ)$ on a Riemannian manifold $(M,g)$ is said to have concurrent potential field if its potential field $v$ is a concurrent vector field. Ricci solitons arisen from concurrent vector fields on Riemannian manifolds were studied recently in \cite{CD2}. The most important concurrent vector field is …

New field invariant refines real spectrum and relates to absolute Galois group.

Study biharmonic vector fields and unit vector fields on Riemannian manifolds.