Geodesics and Translation Curves in <inline-formula><math display="inline"><semantics><msubsup><mi>Sol</mi><mn>0</mn><mn>4</mn></msubsup></semantics></math></inline-formula>

Geodesics and Translation Curves in <inline-formula><math display="inline"><semantics><msubsup><mi>Sol</mi><mn>0</mn><mn>4</mn></msubsup></semantics></math></inline-formula>

A translation curve in a Thurston space is a curve such that for given unit vector at the origin, the translation of this vector is tangent to the curve in every point of the curve. In most Thurston spaces, translation curves coincide with geodesic lines. However, this does not hold for Thurston spa...

Full description

Bibliographic Details
Main Author:	Zlatko Erjavec
Format:	Article
Language:	English
Published:	MDPI AG 2023-03-01
Series:	Mathematics
Subjects:	geodesic translation curve solvable Lie group <named-content content-type="equation"><inline-formula> <mml:math id="mm310000"> <mml:semantics> <mml:msubsup> <mml:mi>Sol</mml:mi> <mml:mn>0</mml:mn> <mml:mn>4</mml:mn> </mml:msubsup> </mml:semantics> </mml:math> </inline-formula></named-content> space
Online Access:	https://www.mdpi.com/2227-7390/11/6/1533

Similar Items

On Translation Curves and Geodesics in <inline-formula><math display="inline"><semantics><msubsup><mrow><mi>Sol</mi></mrow><mn>1</mn><mn>4</mn></msubsup></semantics></math></inline-formula>
by: Zlatko Erjavec, et al.
Published: (2023-04-01)

An Improved Postprocessing Method to Mitigate the Macroscopic Cross-Slice <i>B</i><sub>0</sub> Field Effect on <inline-formula><math display="inline"><semantics><mrow><msubsup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow><mrow><mi>*</mi></mrow></msubsup></mrow></semantics></math></inline-formula> Measurements in the Mouse Brain at 7T
by: Chu-Yu Lee, et al.
Published: (2024-07-01)

Fe<inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold">C</mi><mn mathvariant="bold">4</mn></msub><msubsup><mi mathvariant="bold">H</mi><mn mathvariant="bold">2</mn><mrow><mrow><mn mathvariant="bold">2</mn><mo mathvariant="bold">+</mo></mrow></mrow></msubsup></mrow></semantics></math></inline-formula> Encompassing Planar Tetracoordinate Iron: Structure and Bonding Patterns
by: Shilpa Shajan, et al.
Published: (2024-02-01)

Five Bonds to Carbon through Tri-Coordination in <inline-formula><math display="inline"><semantics><mrow><msub><mrow><mi>Al</mi></mrow><mn>3</mn></msub><msubsup><mi mathvariant="normal">C</mi><mn>3</mn><mrow><mo>−</mo><mo>/</mo><mn>0</mn></mrow></msubsup></mrow></semantics></math></inline-formula>
by: Abdul Hamid Malhan, et al.
Published: (2023-05-01)

Riemannian Structures on <inline-formula> <mml:math id="mm1" display="block"> <mml:semantics> <mml:msubsup> <mml:mi mathvariant="double-struck">Z</mml:mi> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:msubsup> </mml:semantics> </mml:math> </inline-formula>-Manifolds
by: Andrew James Bruce, et al.
Published: (2020-09-01)

The Degradation of Aqueous Oxytetracycline by an O<sub>3</sub>/CaO<sub>2</sub> System in the Presence of <inline-formula><math display="inline"><semantics><mrow><msubsup><mrow><mi mathvariant="bold">HCO</mi></mrow><mn mathvariant="bold">3</mn><mo mathvariant="bold">−</mo></msubsup></mrow></semantics></math></inline-formula>: Performance, Mechanism, Degradation Pathways, and Toxicity Evaluation
by: Zedian Li, et al.
Published: (2024-01-01)

Optimal <named-content content-type="inline-formula"><math display="inline"><semantics><mrow><mi>L</mi><mo>(</mo><mi>d</mi><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></named-content>-Labeling of Certain Direct Graph Bundles Cycles over Cycles and Cartesian Graph Bundles Cycles over Cycles
by: Irena Hrastnik Ladinek
Published: (2024-10-01)

Effect of Strain Rate on Nano-Scale Mechanical Behavior of A-Plane (<inline-formula><math display="inline"><semantics><mrow><mn>11</mn><mover accent="true"><mn>2</mn><mo>¯</mo></mover><mn>0</mn></mrow></semantics></math></inline-formula>) ZnO Single Crystal by Nanoindentation
by: Xiaolin Zhu, et al.
Published: (2023-02-01)

Consistent Estimators of the Population Covariance Matrix and Its Reparameterizations
by: Chia-Hsuan Tsai, et al.
Published: (2025-01-01)

The Norm Function for Commutative <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></semantics></math></inline-formula>-Graded Rings
by: Azzh Saad Alshehry, et al.
Published: (2024-12-01)

<inline-formula><math display="inline"><semantics><msub><mi mathvariant="script">L</mi><mn>1</mn></msub></semantics></math></inline-formula> Adaptive Control Based on Dynamic Inversion for Morphing Aircraft
by: Lingquan Cheng, et al.
Published: (2023-09-01)

<inline-formula><math display="inline"><semantics><msub><mi mathvariant="script">L</mi><mn>1</mn></msub></semantics></math></inline-formula> Adaptive Control for Small-Scale Unmanned Helicopters: Enhancing Speed Regulation
by: Giulia Bertolani, et al.
Published: (2024-11-01)

The Convergence and Boundedness of Solutions to SFDEs with the G-Framework
by: Rahman Ullah, et al.
Published: (2024-01-01)

Simulating Vertical Profiles of Optical Turbulence at the Special Astrophysical Observatory Site
by: Artem Y. Shikhovtsev, et al.
Published: (2024-11-01)

Adaptive Neuro-Fuzzy Control of Active Vehicle Suspension Based on <inline-formula><math display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-italic">H</mi></mrow><mrow><mn mathvariant="bold">2</mn></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-italic">H</mi></mrow><mrow><mstyle mathvariant="bold"><mo>∞</mo></mstyle></mrow></msub></mrow></semantics></math></inline-formula> Synthesis
by: Jaffar Seyyed Esmaeili, et al.
Published: (2023-11-01)

Asymptotic Antipodal Solutions as the Limit of Elliptic Relative Equilibria for the Two- and n-Body Problems in the Two-Dimensional Conformal Sphere
by: Rubén Darío Ortiz Ortiz, et al.
Published: (2024-03-01)

<inline-formula><math display="inline"><semantics><mrow><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi mathvariant="double-struck">C</mi><mo>)</mo></mrow></semantics></math></inline-formula> Scheme Processing of Singularities in Quantum Computing and Genetics
by: Michel Planat, et al.
Published: (2023-02-01)

<inline-formula><math display="inline"><semantics><mrow><msub><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi></mrow></semantics></math></inline-formula> Nanotubes with Negative Strain Energies and Improvements of Thermoelectric Properties via N-Doping Predicted from First-Principle Calculations
by: Jianbao Wu, et al.
Published: (2023-07-01)

Machine Learning Regressors to Estimate Continuous Oxygen Uptakes (<inline-formula><math display="inline"><semantics><mrow><msub><mrow><mover accent="true"><mrow><mi mathvariant="bold-italic">V</mi></mrow><mo>˙</mo></mover><mi mathvariant="bold-italic">O</mi></mrow><mrow><mn mathvariant="bold">2</mn></mrow></msub></mrow></semantics></math></inline-formula>)
by: Daeeon Hong, et al.
Published: (2024-09-01)

<inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">F</mi></semantics></math></inline-formula>-Contractions Endowed with Mann’s Iterative Scheme in Convex <inline-formula><math display="inline"><semantics><msub><mi mathvariant="bold-script">G</mi><mi mathvariant="bold-italic">b</mi></msub></semantics></math></inline-formula>-Metric Spaces
by: Amna Naz, et al.
Published: (2023-09-01)

Local <i>C</i><sup>0,1</sup>-Regularity for the Parabolic <i>p</i>-Laplacian Equation on the Group SU(3)
by: Yongming He, et al.
Published: (2024-04-01)

Conditioning Theory for Generalized Inverse <inline-formula><math display="inline"><semantics><msubsup><mi>C</mi><mi>A</mi><mo>‡</mo></msubsup></semantics></math></inline-formula> and Their Estimations
by: Mahvish Samar, et al.
Published: (2023-04-01)

Second-Order Regularity for Degenerate Parabolic Quasi-Linear Equations in the Heisenberg Group
by: Chengwei Yu, et al.
Published: (2024-11-01)

On Generalizations of the Close-to-Convex Functions Associated with <inline-formula><math display="inline"><semantics><mi mathvariant="fraktur">q</mi></semantics></math></inline-formula>-Srivastava–Attiya Operator
by: Daniel Breaz, et al.
Published: (2023-04-01)

Describing Water Wave Propagation Using the <inline-formula><math display="inline"><semantics><mfrac><msup><mi mathvariant="bold-italic">G</mi><mo mathvariant="bold">′</mo></msup><msup><mi mathvariant="bold-italic">G</mi><mn mathvariant="bold">2</mn></msup></mfrac></semantics></math></inline-formula>–Expansion Method
by: Safoura Rezaei Aderyani, et al.
Published: (2022-12-01)

Modified <named-content content-type="equation"><inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula></named-content>-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry
by: Mohd Danish Siddiqi, et al.
Published: (2024-10-01)

<inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">I</mi></semantics></math></inline-formula>-Symmetric Spaces and the <i>π</i>-Images of Metric Spaces
by: Fang Liu, et al.
Published: (2024-09-01)

<i>n</i><sub>0</sub>-Order Weighted Pseudo Δ-Almost Automorphic Functions and Abstract Dynamic Equations
by: Chao Wang, et al.
Published: (2019-08-01)

Analytical Inverse QCD Coupling Constant Approach and Its Result for <i>α<sub>s</sub></i>
by: Rocco Malaspina, et al.
Published: (2024-08-01)

Analysis and Applications of Some New Fractional Integral Inequalities
by: Sofia Ramzan, et al.
Published: (2023-10-01)

Energy Management of Hydrogen Hybrid Electric Vehicles—Online-Capable Control
by: David Machacek, et al.
Published: (2024-05-01)

Some New Notions of Continuity in Generalized Primal Topological Space
by: Muhammad Shahbaz, et al.
Published: (2024-12-01)

The <inline-formula><math display="inline"><semantics><mrow><msub><mrow><mi mathvariant="bold-script">T</mi></mrow><mrow><mi mathvariant="bold">e</mi></mrow></msub></mrow></semantics></math></inline-formula> Transform: A High-Resolution Integral Transform and Its Key Properties
by: Eduardo Trutié-Carrero, et al.
Published: (2023-10-01)

Application of Fuzzy Subordinations and Superordinations for an Analytic Function Connected with <inline-formula><math display="inline"><semantics><mstyle mathvariant="bold"><mrow><mi mathvariant="fraktur">q</mi></mrow></mstyle></semantics></math></inline-formula>-Difference Operator
by: Ekram E. Ali, et al.
Published: (2025-02-01)

Polynomial Decay of the Energy of Solutions of the Timoshenko System with Two Boundary Fractional Dissipations
by: Suleman Alfalqi, et al.
Published: (2024-08-01)

Teleseismic P-Wave Attenuation Beneath the Arabian Plate
by: Talal Merghelani, et al.
Published: (2023-11-01)

A collection of seminorms linking the <inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">A</mi></semantics></math></inline-formula>-numerical radius and the operator <inline-formula><math display="inline"><semantics><mi mathvariant="bold-script">A</mi></semantics></math></inline-formula>-seminorm
by: Salma Aljawi, et al.
Published: (2024-04-01)

On Modified Interpolative Almost <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">E</mi><mo>−</mo></mrow></semantics></math></inline-formula>Type Contraction in Partial Modular <inline-formula><math display="inline"><semantics><mrow><mi>b</mi><mo>−</mo></mrow></semantics></math></inline-formula>Metric Spaces
by: Dilek Kesik, et al.
Published: (2023-07-01)

Uncovering Hidden Insights with Long-Memory Process Detection: An In-Depth Overview
by: Hossein Hassani, et al.
Published: (2023-06-01)

<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">C</mi></mrow></semantics></math></inline-formula>-Semigroups and Their Induced Order
by: Daniel Marín-Aragón, et al.
Published: (2024-09-01)