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Everything about Volume form
Differential 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 of dimension, a volume form is an -form. It is an element of the space of sections of the line bundle, denoted as. A manifold admits a nowhere-vanishing volume form if and only if it is orientable. An orientable manifold has infinitely many volume forms, since multiplying a volume form by a nowhere-vanishing real valued function yields another volume form. On non-orientable manifolds, one may instead define the weaker notion of a density. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Volume formA 5-minute orientation
- Skim a recent paper: Association of Sleep, Neuropsychological Performance, and Gray Matter Volume With Glymphatic Function in Community-Dwelling Older AdultsInfluential work since 2022
- Pick up a classic book: ONE PIECE 1The most-reprinted book on the subject
- Read the landmark paper: Patterned Paper as a Platform for Inexpensive, Low‐Volume, Portable BioassaysCited 2,669 times
- Go sideways: Frame bundleA closely related topic
- Go sideways: G-structure on a manifoldA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Patterned Paper as a Platform for Inexpensive, Low‐Volume, Portable Bioassays
Form factors in finite volume I: Form factor bootstrap and truncated conformal space
Gauduchon metrics with prescribed volume form
Relationship Between Jaw Muscle Volume and Craniofacial Form
Volume-preserving free-form solids
Resolutions of the prescribed volume form equation
Actin: Volume Change on Transformation of G-Form to F-Form
Sine–Gordon form factors in finite volume
🆕 Influential since 2022
Association of Sleep, Neuropsychological Performance, and Gray Matter Volume With Glymphatic Function in Community-Dwelling Older Adults
Digital image and volume correlation for deformation and damage characterisation of fibre-reinforced composites: A review
Dynamics of the Rabinowitsch fluid in a reduced form of elliptic duct using finite volume method
A Multi-volume constraint approach to diverse form designs from topology optimization
Real-Time Modeling of Volume and Form Dependent Nanoparticle Fractionation in Tubular Centrifuges
📚 Books worth reading
ONE PIECE 1尾田栄一郎 · 1997
ONE PIECE 4尾田栄一郎 · 1998
ONE PIECE 3尾田栄一郎 · 1998
ONE PIECE 10尾田栄一郎 · 1999
ONE PIECE 2尾田栄一郎 · 1998
鋼の錬金術師 1荒川弘 · 2002
ONE PIECE 6尾田栄一郎 · 1998
ONE PIECE 7尾田栄一郎 · 1999
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Frame bundle In mathematics, a frame bundle is a principal fiber bundle F ( E ) {\displaystyle F(E)} associated with any vector bundle E {\displaystyle E} . The fiber…
- 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…
- Cotangent bundle In mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point…
- Almost symplectic manifold In differential geometry, an almost symplectic structure on a differentiable manifold M {\displaystyle M} is a non-degenerate two-form ω {\displaystyle…
- Darboux's theorem In differential geometry, a field in mathematics, Darboux's theorem is a theorem providing a normal form for special classes of differential 1-forms, partially…
- Integration along fibers In differential geometry, the integration along fibers of a k-form yields a ( k − m ) {\displaystyle (k-m)} -form where m is the dimension of the fiber…
- Seiberg–Witten invariants In mathematics, and especially gauge theory, Seiberg–Witten invariants are invariants of compact smooth oriented 4-manifolds introduced by Edward Witten (1994)…
- Momentum map In mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map) is a tool associated with a Hamiltonian action…