Fiber bundles | Manifolds | Vector bundles | Differential topology

Parallelizable manifold

In mathematics, a differentiable manifold of dimension n is called parallelizable if there exist smooth vector fields on the manifold, such that at every point of the tangent vectorsprovide a basis of the tangent space at . Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a global section on A particular choice of such a basis of vector fields on is called a parallelization (or an absolute parallelism) of . (Wikipedia).

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What are parallel lines and a transversal

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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What are the Angle Relationships for Parallel Lines and a Transversal

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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What is the Consecutive Interior Angle Converse Theorem

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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Using the properties of parallelograms to solve for the missing diagonals

👉 Learn how to solve problems with parallelograms. A parallelogram is a four-sided shape (quadrilateral) such that each pair of opposite sides are parallel and are equal. Some of the properties of parallelograms are: each pair of opposite sides are equal, each pair of opposite sides are pa

From playlist Properties of Parallelograms

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What is a parallel universe?

Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu

From playlist Science Unplugged: Parallel Universes

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Hao Xu (7/26/22): Frobenius algebra structure of statistical manifold

Abstract: In information geometry, a statistical manifold is a Riemannian manifold (M,g) equipped with a totally symmetric (0,3)-tensor. We show that the tangent bundle of a statistical manifold has a Frobenius algebra structure if and only if the sectional K-curvature vanishes. This gives

From playlist Applied Geometry for Data Sciences 2022

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Riemannian Geometry - Examples, pullback: Oxford Mathematics 4th Year Student Lecture

Riemannian Geometry is the study of curved spaces. It is a powerful tool for taking local information to deduce global results, with applications across diverse areas including topology, group theory, analysis, general relativity and string theory. In these two introductory lectures

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Proving Parallel Lines with Angle Relationships

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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What is the Corresponding Angle Converse Theorem

👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i

From playlist Parallel Lines and a Transversal

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What are the properties that make up a parallelogram

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From playlist Properties of Parallelograms

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Johannes Ebert - Rigidity theorems for the diffeomorphism action on spaces of metrics of (...)

The diffeomorphism group $\mathrm{Diff}(M)$ of a closed manifold acts on the space $\mathcal{R}^+ (M)$ of positive scalar curvature metrics. For a basepoint $g$, we obtain an orbit map $\sigma_g: \mathrm{Diff}(M) \to \mathcal{R}^ (M)$ which induces a map $(\sigma_g)_*:\pi_*( \mathrm{Diff}(

From playlist Not Only Scalar Curvature Seminar

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Holomorphic Curves in Compact Complex Parallelizable Manifold Γ\SL(2, C) by Ryoichi Kobayashi

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Michael Atiyah, Seminars Geometry and Topology 1/2 [2009]

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From playlist Mathematics

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What is a tangent plane

The "tangent plane" of the graph of a function is, well, a two-dimensional plane that is tangent to this graph. Here you can see what that looks like.

From playlist Multivariable calculus

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Jamie Scott (9/23/21): Applications of Surgery to a Generalized Rudyak Conjecture

Rudyak’s conjecture states that cat (M) is at least cat (N) given a degree one map f between the closed manifolds M and N. In the recent paper "Surgery Approach to Rudyak's Conjecture", the following theorem was proven: Theorem. Let f from M to N be a normal map of degree one between clos

From playlist Topological Complexity Seminar

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Pre-recorded lecture 15: gl-regular Nijenhuis operators (part 4)

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Alexander Dranishnikov (9/22/22): On the LS-category of group homomorphisms

In 50s Eilenberg and Ganea proved that the Lusternik-Schnirelmann category of a discrete group Γ equals its cohomological dimension, cat(Γ) = cd(Γ). We discuss a possibility of the similar equality cat(φ) = cd(φ) for group homomorphisms φ : Γ → Λ. We prove this equality for some classes of

From playlist Topological Complexity Seminar

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Branched Holomorphic Cartan Geometries by Sorin Dumitrescu

DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be

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Parallelograms - Geometry

This geometry video tutorial provides a basic introduction into parallelograms. It explains the properties of parallelograms and how to use it calculate the missing sides and missing angles of parallelograms. It contains plenty of examples and practice problems for you to work on. Oppo

From playlist Geometry Video Playlist

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Lecture 5: Equivariant CNNs II (Riemannian manifolds) - Maurice Weiler

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From playlist First Italian School on Geometric Deep Learning - Pescara 2022

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