Structures on manifolds | Riemannian geometry | Differential geometry

G2 manifold

In differential geometry, a G2 manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2. The group is one of the five exceptional simple Lie groups. It can be described as the automorphism group of the octonions, or equivalently, as a proper subgroup of special orthogonal group SO(7) that preserves a spinor in the eight-dimensional spinor representation or lastly as the subgroup of the general linear group GL(7) which preserves the non-degenerate 3-form , the associative form. The Hodge dual, is then a parallel 4-form, the coassociative form. These forms are calibrations in the sense of Reese Harvey and H. Blaine Lawson, and thus define special classes of 3- and 4-dimensional submanifolds. (Wikipedia).

Video thumbnail

Manifolds 1.3 : More Examples (Animation Included)

In this video, I introduce the manifolds of product manifolds, tori/the torus, real vectorspaces, matrices, and linear map spaces. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5koj5

From playlist Manifolds

Video thumbnail

Overview of gauge theory and submanifold geometry on G_2 manifolds - Simon Donaldson [2014]

Name: Simon Donaldson Event: Program: G2 manifolds Event URL: view webpage Title: Overview of gauge theory and submanifold geometry on G_2 manifolds, I Date: 2014-08-19 @3:30 PM

From playlist Mathematics

Video thumbnail

What is a Manifold? Lesson 6: Topological Manifolds

Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.

From playlist What is a Manifold?

Video thumbnail

What is a manifold?

I define topological manifolds. Motivated by the prospect of calculus on topological manifolds, I introduce smooth manifolds. At the end I point out how one needs to change the definitions, to obtain C^1 or even complex manifolds. To learn more about manifolds, see Lee's "Introduction to

From playlist Differential geometry

Video thumbnail

Manifolds 1.2 : Examples of Manifolds

In this video, I describe basic examples of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/IZO0G25

From playlist Manifolds

Video thumbnail

What is a G Chord?

A review of the notes common to all formations of a G chord.

From playlist Music Lessons

Video thumbnail

Manifolds #5: Tangent Space (part 1)

Today, we introduce the notion of tangent vectors and the tangent vector space at a point on a manifold.

From playlist Manifolds

Video thumbnail

Orientations for Moduli Spaces in Higher-Dimensional Gauge Theory by Markus Upmeier

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

From playlist Analytic and Algebraic Geometry-2018

Video thumbnail

An Oxford Mathematics Graduate Supervision - Geometry and Physics in 7 Dimensions

So how do supervisor & graduate student work together? What happens in a graduate supervision? To find out, we filmed a supervision. Introducing Professor Jason Lotay & graduate student Izar Alonso Lorenzo as they discuss geometry in seven dimensions related to special holonomy, gauge the

From playlist Oxford Mathematics Student Tutorials and Graduate Supervisions

Video thumbnail

Lorenzo Foscolo: ALC manifolds with exceptional holonomy

We will describe the construction of complete non-compact Ricci-flat manifolds of dimension 7 and 8 with holonomy $G_{2}$ and Spin(7) respectively. The examples we consider all have non-maximal volume growth and an asymptotic geometry, so-called ALC geometry, that generalises to higher dim

From playlist Geometry

Video thumbnail

Exceptional holonomy and related geometric structures: Examples and moduli theory - Simon Donaldson

Marston Morse Lectures Topic: Exceptional holonomy and related geometric structures: Examples and moduli theory. Speaker: Simon Donaldson Affiliation: Stonybrook University Date: April 4, 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Periodic Foams and Manifolds - Frank Lutz

Frank Lutz Technische Universitat Berlin March 2, 2011 WORKSHOP ON TOPOLOGY: IDENTIFYING ORDER IN COMPLEX SYSTEMS For more videos, visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Robert BRYANT - Algebraically Constrained Special Holonomy Metrics...

Robert BRYANT - Algebraically Constrained Special Holonomy Metrics and Second-order Associative 3-folds There are various methods known now for constructing more-or-less explicit metrics with special holonomy; most of these rely on assumptions of symmetry and/or reduction. Another promisi

From playlist Riemannian Geometry Past, Present and Future: an homage to Marcel Berger

Video thumbnail

Pre-recorded lecture 22: Open problems (part 2)

MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet

From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)

Video thumbnail

Manifolds 1.1 : Basic Definitions

In this video, I give the basic intuition and definitions of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Manifolds

Video thumbnail

Exceptional holonomy and related geometric structures: Dimension reduction...- Simon Donaldson

Marston Morse Lectures Topic: Exceptional holonomy and related geometric structures: Dimension reduction and boundary value problems Speaker: Simon Donaldson Affiliation: Stonybrook University Date: April 6, 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

What is a Manifold? Lesson 2: Elementary Definitions

This lesson covers the basic definitions used in topology to describe subsets of topological spaces.

From playlist What is a Manifold?

Video thumbnail

S. Donaldson - Boundary value problems for $G_2$ structures

In the lecture we consider the existence of G2 structures on 7-manifolds with boundary, with prescribed data on the boundary. In the first part we will review general background and theory, including Hitchin’s variational approach. We will then discuss in more detail reductions of the pr

From playlist Complex analytic and differential geometry - a conference in honor of Jean-Pierre Demailly - 6-9 juin 2017

Related pages

Pontryagin class | G2 (mathematics) | Supersymmetry | String theory | Calibrated geometry | Betti number | Group (mathematics) | Simple Lie group | Spin(7)-manifold | Spinor | General linear group | Marcel Berger | Supermultiplet | Riemannian manifold | Fundamental group | Automorphism group | Differential geometry | Supergravity | Calabi–Yau manifold