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Everything about Tangent bundle
Tangent spaces of a manifold
A tangent bundle is the collection of all of the tangent spaces for all points on a manifold, structured in a way that it forms a new manifold itself. Formally, in differential geometry, the tangent bundle of a differentiable manifold is a manifold which assembles all the tangent vectors in. As a set, it is given by the disjoint union of the tangent spaces of. That is, Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Tangent bundleA 5-minute orientation
- Skim a recent paper: Examples of Fano manifolds with non‐pseudoeffective tangent bundleInfluential work since 2022
- Pick up a classic book: Threefolds with semipositive tangent bundleThe most-reprinted book on the subject
- Read the landmark paper: On the Geometry of the Tangent Bundle.Cited 222 times
- Go sideways: Differentiable manifoldA closely related topic
- Go sideways: Cotangent spaceA closely related topic
📖 Definitions
Noun A fiber bundle for which the base space is a differentiable manifold and each fiber over a point of that manifold is the tangent space of that point.
🏆 Landmark papers (most cited)
On the Geometry of the Tangent Bundle.
Tangent bundle geometry Lagrangian dynamics
Structure of spacetime tangent bundle
Finslerian Fields in the Spacetime Tangent Bundle
Riemann curvature scalar of spacetime tangent bundle
Uniruled varieties with split tangent bundle
Complex spacetime tangent bundle
Differential geometry of spacetime tangent bundle
🆕 Influential since 2022
Examples of Fano manifolds with non‐pseudoeffective tangent bundle
Stability of the tangent bundle through conifold transitions
Fano manifolds with big tangent bundle: a characterisation of $$V_5$$
Projective manifolds whose tangent bundle is Ulrich
Anisotropic conformal dark gravity on the Lorentz tangent bundle spacetime
📚 Books worth reading
- 📕Threefolds with semipositive tangent bundleDonu Arapura · 1985
- 📕Introduction to microlocal analysisMasaki Kashiwara · 1986
- 📕Tangent and cotangent bundlesYano, Kentarō · 1973
Tangent and cotangent bundlesKentaro Yano · 1973- 📕Some characteristic invariants of foliated bundlesGrzegorz Andrzejczak · 1984
- 📕Eine Invariante für stabil parallelisierte MannigfaltigkeitenMatthias Kreck · 1973
Tangent Structures in Geometry and Their ApplicationsVladimir Balan, Maido Rahula · 2013
The method of iterated tangents with applications in local Riemannian geometryJ. Enrico White · 1982
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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