Concept

Scalar curvature

Related lectures (30)

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Explores normal curvature on a surface, discussing oriented curvature, existence proofs, and elimination methods for finding curvature.

Curvature and Inflection Points

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Gaussian Curvature in Plates

Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.

Curvature and Osculating Circle

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Plates II: Mechanics of Slender Structures

Explores the mechanics of slender structures, discussing plate evaluation, bending energy, and curvature tensors.

Minimal Surfaces and Discrete Differential Geometry

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

Differential Geometry: Parametric Curves & Surfaces

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

Geodesic Curves: Minimizing Distance and Constant Speed

Covers geodesic curves parameterized at constant speed to minimize distances between points.

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.

Curvature and Oriented Curvature

Explores the concepts of curvature, oriented curvature, and inflection points in regular curves.

Gothic Surfaces: Curvature, Development, and Stereotomy

Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.

Weingarten Application of Regular Surfaces

Covers the application of the Weingarten map on regular surfaces and the shape operator.

Beams: Forces, Stresses, and Deformations

Analyzes beams, forces, stresses, deformations, curvature, deflection, and rigidity.

Surfaces with Constant Curvature

Explores surfaces with constant curvature, emphasizing the significance of minimal oriented radius and the properties of pseudo-spheres.

Altitude Models: Derivative Variables

Covers global relief indicators, altitude models, slope, orientation, curvature, and morphological indices for terrain description.

Linear Shell Theory: Equilibrium Equations

Covers the dimensional reduction of strain energy from 3D to 2D and linear shell theory equilibrium equations.

Plates III: Mechanics of Slender Structures

Covers the equations of plates, bending and stretching energy, von Karman equations, and buckling of plates.

Basics of Modern Cosmology - 2

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

Plates III: Buckling Theory and Applications

Explores Föppl-von Kármán plate theory, including buckling equations and an example of plate compression.