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Everything about Parallel transport
System of moving vectors in differential geometry
In differential geometry, parallel transport is a way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with an affine connection, then this connection allows one to transport vectors of the manifold along curves so that they stay parallel with respect to the connection. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Parallel transportA 5-minute orientation
- Skim a recent paper: VistaGPT: Generative Parallel Transformers for Vehicles With Intelligent Systems for Transport AutomationInfluential work since 2022
- Pick up a classic book: High speed civil transport aerodynamic optimizationThe most-reprinted book on the subject
- Read the landmark paper: Parallel and perpendicular transport in multilayered structuresCited 97 times
- Go sideways: Affine connectionA closely related topic
- Go sideways: Riemannian manifoldA closely related topic
📖 Definitions
Noun A way of transporting geometrical data along smooth curves in a manifold.
🏆 Landmark papers (most cited)
Parallel and perpendicular transport in multilayered structures
Convective–diffusive transport in parallel lamination micromixers
Multiplexed Parallel Single Transport Recordings on Nanopore Arrays
Parallel Transport Tractography
Fluid transport by cilia between parallel plates
Parallel Transport Frame for Fiber Shape Sensing
Parallel transport and defects on nematic shells
Parallel transport and band theory in crystals
🆕 Influential since 2022
VistaGPT: Generative Parallel Transformers for Vehicles With Intelligent Systems for Transport Automation
Benefits of Parallel Hybrid Electric Propulsion for Transport Aircraft
An efficient parallel algorithm of variational nodal method for heterogeneous neutron transport problems
Thermal transport analysis of squeezing hybrid nanofluid flow between two parallel plates
Emergent parallel transport and curvature in Hermitian and non-Hermitian quantum mechanics
📚 Books worth reading
- 📕High speed civil transport aerodynamic optimizationJames S. Ryan · 1994
- 📕Nonlinear stability of supersonic jetsR. S. Bhatt · 1995
- 📕Parallelʹnye vychisleni͡ia dl͡ia uravneni͡ia Bolʹ͡tsmana pri deterministicheskom integrirovaniiV. V. Aristov · 1998
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Affine connection In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector…
- Riemannian manifold In differential geometry, a Riemann space (or Riemannian manifold) is a geometric space on which many geometric notions such as distance, angles, length…
- Levi-Civita connection In Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine…
- Finsler manifold In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold M where a (possibly asymmetric) Minkowski norm F(x…
- Covariant derivative In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative…
- Geodesic In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points…
- Connection (vector bundle) In mathematics, and especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport…
- Affine differential geometry In differential geometry, affine differential geometry is the study of differential invariants of curves, surfaces, and higher-dimensional submanifolds…