Riemann curvature tensor

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Related lectures (32)

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Shells I: Mechanics of Slender Structures

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Minimal Surfaces and Discrete Differential Geometry

Explores minimal surfaces, curvature, Laplace-Beltrami operator, numerical solutions, Laplacian smoothing, diffusion flow, and time integration.

Riemann Tensor and Ricci Scalar

Covers the properties of the Riemann tensor and Ricci scalar in normal coordinates.

Flat Space-Time: Conditions and Theorems

Covers the necessary conditions and theorems to have flat space-time and discusses the symmetry properties of the Riemann tensor.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Symmetries and Conservation Laws

Explores Killing vectors, conserved quantities, symmetric spaces, and the Riemann curvature tensor properties.

General Covariance in Gravitational Field

Explores general covariance, Riemann tensor, Bianchi identities, and Einstein tensor in gravitational field.

Exponential Map and Curvature Tensor

Covers the exponential map, covariant derivatives, connection coefficients, and Riemann curvature tensor.

Harmonic Forms and Riemann Surfaces

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Basics of Modern Cosmology - 2

Explores luminosity distance, the Einstein field equation, Stephen Hawking's contributions, and the cosmological principle, among other cosmological concepts.