Backlund transformations of admissible curves in the Galilean 3-space and pseudo-Galilean 3-space and also spatial Backlund transformations of space curves in Galilean 4-space preserve the torsions under certain assumptions.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “Galilean 3-space”
Five types of translation surfaces with constant curvature found in Galilean 3-space.
problem Identifying translation surfaces with constant curvature in Galilean 3-space.
method Examining five types of translation surfaces based on the planarity of translating curves and absolute figure.
result Constant curvature translation surfaces with arbitrary Gaussian and mean curvature are found.
In this paper, space and timelike admissible Smarandache curves in the pseudo- Galilean 3-space are investigated. Also, Smarandache curves of the position vector of space and timelike arbitrary curve and some of its special curves in the pseudo- Galilean 3-space are obtained. To confirm our main results, some examples …
Study classifies magnetic curves in Galilean space tied to Killing vectors.
problem Classifying magnetic curves in Galilean space.
method Complete classification of magnetic curves associated to Killing vector fields.
result Completely classified magnetic curves in Galilean 3-space.
In the present paper, we consider a position vector of an arbitrary curve in the three-dimensional Galilean 3-space. Furthermore, we give some conditions on the curvatures of this arbitrary curve to study special curves and their Smarandache curves. Finally, in the light of this study, some related examples of these cu…
In this paper, we focus on some characterizations for curves in the Galilean and Pseudo-Galilean space.
The aim of this work is to study the Mannheim curves in 3-dimensional Galilean and Pseudo - Galilean space. We obtain the characterizations between the curvatures and torsions of the Mannheim partner curves.
Abstract In this paper, definition of involute-evolute curve couple in Galilean space is given and some well-known theorems for the involute-evolute curves are obtained in 3-dimensional Galilean space.
New Galilean spacetimes found as pp-wave reductions.
problem Understanding isotropic homogeneous Galilean spacetimes.
method Null reductions of pp-wave spacetimes.
result Found novel torsional Galilean spacetimes.
Characterizes Lie groups with specific structures and finds a correspondence between carrollian and galilean Lie algebras.
problem Understanding Lie groups with specific structures.
method Using structure theory of metric Lie algebras and defining new Lie algebras with skew-symmetric derivations.
result A canonical correspondence between carrollian and galilean Lie algebras mediated by bargmannian Lie algebras.
Galilean geometry of motionsmath.DG
In this paper we show that Galilean group is a matrix Lie group and find its structure. Then provide the invariants of special Galilean geometry of motions, by Olver's method of moving coframes, we also find the corresponding structure.
Defined Fermi-Walker derivative in Galilean space and its applications.
problem Defining and applying Fermi-Walker derivative in Galilean space.
method Defined Fermi-Walker derivative in Galilean space , and investigated conditions for Fermi-Walker transport and non-rotating frame along curves.
result Conditions for Fermi-Walker transport and non-rotating frame were investigated in Galilean space.
The paper studies elastic lines on surfaces in Galilean space.
problem Characterizing elastic lines on oriented surfaces in Galilean space.
method Developed Euler-Lagrange equations and used variational method.
result Investigated whether relaxed elastic curves lie on geodesics.
Study finds new factorable surfaces with non-zero curvature in pseudo-Galilean space.
problem Classifying surfaces with non-zero curvature in pseudo-Galilean space.
method Analyzing factorable surfaces as graphs of product functions.
result New classification results for factorable surfaces with non-zero Gaussian and mean curvature.
The paper characterizes curves in pseudo-Galilean 4-space.
problem Characterizing curves in the pseudo-Galilean 4-space .
method Investigation and characterisation of admissible curves in terms of curvature functions.
result Necessary and sufficient conditions for admissible rectifying curves in .
The paper proves no homothetical surfaces exist in 3D pseudo-Galilean space.
problem Exploring homothetical surfaces in pseudo-Galilean space.
method Analyzing surfaces defined by a function and satisfying specific Laplacian conditions.
result No homothetical surfaces exist in 3D pseudo-Galilean space.
The paper studies curves of constant-ratio in pseudo-Galilean space.
problem Characterizing curves of constant-ratio in pseudo-Galilean space.
method Analyzing spacelike curves with constant-ratio in terms of curvature functions.
result Characterization of special curves of constant-ratio in pseudo-Galilean space.
Study inextensible flows of curves in 4D pseudo-Galilean space and defines energy functions.
problem Analyzing inextensible flows and energy of curves in 4D pseudo-Galilean space.
method Expressed inextensible flows as partial differential equations, defined directional derivatives, and expressed bending elastic energy functions.
result Necessary and sufficient conditions for inextensible flows are given as partial differential equations.
The aim of this paper is to study the Mannheim partner curves in three dimensional Galilean space . Some well known theorems are obtained related to Mannheim curves.
We defined normal and rectifying curves in Pseudo-Galilean Space G_3^1. Also we obtained some characterizations of this curves in G_3^1.
This paper is devoted to the study of AW(k)-type curves according to the equiform differential geometry of the pseudo-Galilean space. We show that equiform Bertrand curves are circular helices or isotropic circles of the pseudo-Galilean space. Also, there are equiform Bertrand curves of AW(3) and weak AW(3)-types. More…
The Galilean group is the group of symmetries of Newtonian mechanics, with Lie a lgebra $\gal(n)$. We find algebraically independent generators for the center of the universal enveloping algebra of $\gal(n)$ using coadjoint orbits.
The paper classifies intrinsic torsion in various spacetime structures.
problem Classifying intrinsic torsion in different spacetime structures.
method Review and classification of intrinsic torsion in galilean, Carrollian, Aristotelian, and Bargmannian spacetime structures.
result Found 16 classes for Aristotelian structures and 27 for Bargmannian structures.
We express the first jet bundle of curves in Euclidean space as homogeneous spaces associated to a Galilean-type group. Certain Cartan connections on a manifold with values in the Lie algebra of the Galilean group are characterized as geometries associated to systems of second order ordinary differential equations. We …
Study -brane Galilean and Carrollian geometries via intrinsic torsion.
problem Characterize -brane Galilean and Carrollian geometries via intrinsic torsion.
method Analyze intrinsic torsions as representations of , interpret geometrically, and use physics-inspired methods.
result Recover classification of -brane Galilean geometries and relate to ()-brane Carrollian geometries.
Special curves and their characterizations are one of the main area of mathematicians and physicians. As a special curve we will mainly focus on Mannheim curve which has the following relation: k1=β(k1^2+k2^) where k1 and k2 are curvature and torsion, respectively. In the present paper we define Mannheim curves for 4-d…
The following three geometrical structures on a manifold are studied in detail: (1) Leibnizian: a non-vanishing 1-form plus a Riemannian metric $\h$ on its annhilator vector bundle. In particular, the possible dimensions of the automorphism group of a Leibnizian G-structure are characterized. (2) Galilean: Leibnizi…
Rotation minimizing frames and spherical curves in simply isotropic and pseudo-isotropic 3-spacesmath.DG
The paper develops RM frames for isotropic and pseudo-isotropic spaces and characterizes spherical curves.
problem Differential geometry of curves in isotropic and pseudo-isotropic 3-spaces.
method Developing rotation minimizing frames and applying them to spherical curves in isotropic and pseudo-isotropic spaces.
result Characterization of spherical curves via linear equations involving curvatures and RM frames.
In this paper, first and second type admissible Mannheim partner curves are defined in pseudo-Galilean space . Moreover, it is proved that the distance between the reciprocal points of both of first and second type admissible Mannheim curves and the torsions of these curves are constant. Furthermore, the relatio…
A Kinematic and Geometric Analysis of Trochoidal Wavesphysics.flu-dyn
Analyzes Gerstner's trochoidal waves and their geometric properties.
problem Understanding the geometry and kinematics of trochoidal waves.
method Derives velocity and arc length conditions for cycloidal, curtate, and prolate trochoids using Galilean transformations.
result Conditions for arc lengths of prolate and curtate trochoids to coincide over a wave cycle.
Introduces -Lie groups and studies their symplectic structures and reductions.
problem Developing a theoretical framework for space-time transformations.
method Introduces -Lie groups and studies their canonical -symplectic structures and reductions.
result Poisson reduction under cotangent lifted action of can be described using Lie algebra structures.
Study of homogeneous spacetimes with isotropic symmetry and their symmetries.
problem Classifying and analyzing the geometry and symmetries of homogeneous spacetimes.
method Detailed calculation of symmetries, soldering form, vielbein, and invariant connections for spatially isotropic homogeneous spacetimes.
result Boosts act with generic non-compact orbits and determine infinite-dimensional symmetries reminiscent of BMS Lie algebras.
In this paper, we apply the method of approximate transformation groups proposed by Baikov, Gaziziv and Ibragimov, to compute the first-order approximate symmetry for the Gardner equations with the small parameters. We compute the optimal system and analyze some invariant solutions of These types of equations. Particul…
The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance la…
New concept of Lorentzian-Euclidean black holes and metric transitions explored.
problem Signature-changing spacetimes and their geometric properties.
method Introduction and analysis of Lorentzian-Euclidean black holes and transitions.
result Consistency of proper time to horizon in Lorentzian-Euclidean black holes.
In this paper, the equations governing the unsteady flow of a perfect polytropic gas in three space dimensions are considered. The basic similarity reductions for this system are performed. Reduced equations and exact solutions associated with the symmetries are obtained. This results is used to give the invariance of …
Complete classification of surfaces with a canonical principal direction in the Minkowski 3-spacemath.DG
Paper classifies surfaces with a special direction in Minkowski 3-space.
problem Characterizing surfaces with a canonical principal direction.
method Characterization and classification of surfaces in Minkowski 3-space.
result All surfaces with a canonical principal direction are classified.
Unified framework for Alexandrov 3-spaces, extending manifold results.
problem Extend manifold topology results to Alexandrov 3-spaces.
method Generalize connected sum, prime decomposition, and Dehn surgery.
result Unified framework for Alexandrov 3-spaces, including non-manifold spaces.
The paper describes and classifies surfaces in isotropic 3-space.
problem Characterizing surfaces in isotropic 3-space.
method Analyzes Weingarten and linear Weingarten surfaces in \mathbb{I}^{3} using the position vector and Laplace operator.
result Classifies surfaces in \mathbb{I}^{3} satisfying certain equations.
We show existence of constant mean curvature 1 surfaces in both hyperbolic 3-space and de Sitter 3-space with two complete embedded ends and any positive genus up to genus twenty. We also find another such family of surfaces in de Sitter 3-space, but with a different non-embedded end behavior.
In this paper, we firstly introduce the group of similarity transformations in the Minkowski-3 space. We describe differential- geometric invariants of a non-lightlike curve according to the group of similarity transformations of the Minkowski 3-space. We show extension of fundamental theorem for non-lightlike curves u…
We make observations about constant mean curvature surfaces in Euclidean 3-space and their dual surfaces, and the resulting pairs of surfaces in hyperbolic 3-space under the Lawson correspondence.
Proves embedding condition for certain 2-complexes in 3-space.
problem Embedding simply connected 2-complexes in 3-space.
method Analyzes link graphs and their embeddings in the plane.
result Trivial first homology group implies embedding in 3-space.
Study space-like loxodromes on canal surfaces in Minkowski 3-space.
problem Characterizing space-like loxodromes on canal surfaces.
method Solving differential equations for space-like loxodromes on canal surfaces in Minkowski 3-space.
result Differential equations for space-like loxodromes on canal surfaces.
A new model uses complex quaternions for hyperbolic 3-space.
problem No specific problem stated; focuses on a new model.
method Developed a model using complex quaternions for real hyperbolic 3-space.
result Introduced new computational tools for studying hyperbolic isometries.
It is shown that timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL(2,R) via Bryant type representation formulae. These formulae are used to investigate an explicit one-to-one correspondence, the s…
Sharp inequality proved in 3D hyperbolic spaces using flow methods.
problem Proving a sharp Minkowski-type inequality in Cartan-Hadamard 3-spaces.
method Using harmonic mean curvature flow to prove the inequality.
result Sharpened estimates for total mean curvature in hyperbolic 3-space.
Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-spacemath.DG
We construct embedded triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space with the same topology as the Schwarz D surface in the Euclidean 3-space.