Lectures related to Differential Geometry: Curves

Covers the geometric properties of hyperbolic paraboloids and hyperboloids, focusing on their construction and curvature characteristics.

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

Explores the Frenet-Serret formulas for curvature and torsion in three-dimensional space.

Covers the fundamentals of differential geometry of surfaces, including the equilibrium of shells, pressure vessels, and the curvature of surfaces.

Explores surfaces with variable curvature, discussing their construction and properties.

Explores geometric surfaces, rules between shapes, and architectural applications.

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

Examines geometric singularities in architectural design through the analysis of spatial intersections.