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Everything about Frame bundle
Principal bundle associated to a vector bundle
In mathematics, a frame bundle is a principal fiber bundle associated with any vector bundle. The fiber of over a point is the set of all ordered bases, or frames, for. The general linear group acts naturally on via a change of basis, giving the frame bundle the structure of a principal -bundle. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Frame bundleA 5-minute orientation
- Skim a recent paper: MetaVRain: A Mobile Neural 3-D Rendering Processor With Bundle-Frame-Familiarity-Based NeRF Acceleration and Hybrid DNN ComputingInfluential work since 2022
- Pick up a classic book: Differential geometry of frame bundlesThe most-reprinted book on the subject
- Read the landmark paper: Determination of Phobos’ rotational parameters by an inertial frame bundle block adjustmentCited 24 times
- Go sideways: Kosmann liftA closely related topic
- Go sideways: Associated bundleA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Determination of Phobos’ rotational parameters by an inertial frame bundle block adjustment
Frame Bundle of Riemannian Path Space and Ricci Tensor in Adapted Differential Geometry
Lifts of tensor fields to the frame bundle
Modelling anisotropic covariance using stochastic development and sub-Riemannian frame bundle geometry
Quality assessment for GPS‐supported bundle block adjustment based on aerial digital frame imagery
Complete Lifts of Tensor Fields and Connections to the Frame Bundle
A frame bundle generalization of multisymplectic geometries
NUVO Space I: Unit-Constrained Frame Bundle and Conformal Scalar
🆕 Influential since 2022
MetaVRain: A Mobile Neural 3-D Rendering Processor With Bundle-Frame-Familiarity-Based NeRF Acceleration and Hybrid DNN Computing
Novel theorems for metallic structures on the frame bundle of the second order
BA-LINS: A Frame-to-Frame Bundle Adjustment for LiDAR-Inertial Navigation
An 197-μJ/Frame Single-Frame Bundle Adjustment Hardware Accelerator for Mobile Visual Odometry
Characterizations of the Frame Bundle Admitting Metallic Structures on Almost Quadratic ϕ-Manifolds
📚 Books worth reading
Differential geometry of frame bundlesL. A. Cordero · 1989
Engineering ArchitectureYasmin Sabina Khan · 2004- 📕Geometric aspects of stochastic delay differential equations on manifoldsPedro J. Catuogno, Paulo R. C. Ruffino · 2002
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Kosmann lift In differential geometry, the Kosmann lift, named after Yvette Kosmann-Schwarzbach, of a vector field X {\displaystyle X\,} on a Riemannian manifold (…
- Associated bundle In mathematics, the theory of fiber bundles with a structure group G {\displaystyle G} (a topological group) allows an operation of creating an associated…
- G-structure on a manifold In differential geometry, a G-structure on an n {\displaystyle n} -manifold M {\displaystyle M} , for a given structure group G {\displaystyle G} , is…
- Clifford bundle In mathematics, a Clifford bundle is an algebra bundle whose fibers have the structure of a Clifford algebra and whose local trivializations respect the…
- Lie algebroid In mathematics, a Lie algebroid is a vector bundle A → M {\displaystyle A\rightarrow M} together with a Lie bracket on its space of sections Γ ( A ) {\displayst…
- Volume form In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold…
- Quaternionic manifold In differential geometry, a quaternionic manifold is a quaternionic analog of a complex manifold. The definition is more complicated and technical than…
- Contact bundle In differential geometry, a contact bundle is a particular type of fiber bundle constructed from a smooth manifold. Like how the tangent bundle is the…