Concept

Metric tensor

Related lectures (30)

Explores implicit surface parametrizations and the use of metric tensors in surface parameterization.

Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.

Metric Tensor: Definition

Explores the definition and properties of the metric tensor, enabling control of geometric quantities and lengths.

Second Fundamental Tensor

Explores the second fundamental tensor and its role in calculating normal curvature on surfaces.

Linear Shell Theory: Equilibrium and Energy

Covers the expression of the Kirchhoff-Saint Venant energy in a covariant setting and explores equilibrium equations for spherical shells and linear shell theory.

Lecture 5: Conformal Transformations

Explores Conformal Transformations, emphasizing scale transformations and correlation functions.

Intersection of Manifolds in Exercise 8.2

Covers the intersection of manifolds in exercise 8.2 and fiscal year 8.8.

Stereographic Projection and Metric Tensors

Explores stereographic projection and metric tensors on hyperbolic planes, emphasizing isometry and conforming models.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Spherically Symmetric Metrics

Explores spherically symmetric metrics in flat space and their implications in gravity and spacetime.

Gauss Theorem in R^n+1

Explores the Gauss theorem in R^n+1, covering regular domains, vector fields, surface integrals, and volume calculations.

Solid Dynamics: Laws and Variants

Explores laws of dynamics, angular momentum, inertia tensor, and kinetic energy.

Hodge Duality and Covariant Derivatives

Introduces Hodge duality, covariant derivatives, and key concepts in differential geometry.

Tensors and Normal Coordinates

Introduces one-forms, tensors, normal coordinates, and metric tensors in differential geometry.

Deformation Analysis in Elastic Solids

Explores manipulation of 3D arrays, barycenters, shape matrices, Jacobians, eigendecomposition, and visualization in elastic solids.

Developable Surfaces and Parametrization

Explores developable surfaces, parametrization, equations verification, and conformally flat surfaces.

Inertia Tensor and Rotational Dynamics

Explores inertia tensor, main axes of inertia, and rotational dynamics of solids, including Steiner's theorem and balancing techniques.

Physics 1: Inertia Tensor Calculation

Covers the calculation of the inertia tensor for a thin ring, with examples demonstrating the process.

Tensors and Lorentz Transformations

Covers tensors, Lorentz transformations, and electrodynamics in relativistic notation.

Static Isotropic Metric

Explores static isotropic metric properties and equations in physics, focusing on the behavior outside the gravitational field.