dg.differential geometry - Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature - MathOverflow
By A Mystery Man Writer
Description
A curve in the plane is determined, up to orientation-preserving
Euclidean
motions, by its curvature function, $\kappa(s)$.
Here is one of my favorite examples, from
Alfred Gray's book,
Modern
![dg.differential geometry - Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature - MathOverflow](https://i.ytimg.com/vi/iTZKKh9_CT8/hq720.jpg?sqp=-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD&rs=AOn4CLD2uwrGCi7HHSpMLjxj4EYPHWclCg)
Lecture 15: Curvature of Surfaces (Discrete Differential Geometry
![dg.differential geometry - Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature - MathOverflow](https://i.ytimg.com/vi/gFS4ntMy_zM/maxresdefault.jpg)
Differential Geometry: Lecture 12 part 1: surfaces in R3
![dg.differential geometry - Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature - MathOverflow](https://i.stack.imgur.com/tMFPd.png)
differential geometry - The curvature of an intersection curve
![dg.differential geometry - Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature - MathOverflow](https://solitaryroad.com/c335/ole3.gif)
Geodesics, geodesic curvature, geodesic parallels, geodesic
What are applications of convex sets and the notion of convexity
![dg.differential geometry - Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature - MathOverflow](https://i.ytimg.com/vi/pLv1a8KAbuk/sddefault.jpg)
Differential Geometry: Lecture 21 part 2: total Gaussian curvature
![dg.differential geometry - Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature - MathOverflow](https://i.ytimg.com/vi/mrXyot5WGCQ/hq720.jpg?sqp=-oaymwE7CK4FEIIDSFryq4qpAy0IARUAAAAAGAElAADIQj0AgKJD8AEB-AHUBoAC4AOKAgwIABABGGAgYChgMA8=&rs=AOn4CLAeTZzEmVwa265kAYjxUUqf_U-0aQ)
Differential Geometry: calculating Gaussian and Mean Curvature two
![dg.differential geometry - Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature - MathOverflow](https://images.slideplayer.com/26/8672976/slides/slide_19.jpg)
Geometric Modeling using Polygonal Meshes Lecture 3: Discrete
![dg.differential geometry - Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature - MathOverflow](https://cdn.britannica.com/20/70820-004-1DBEF24F/surface-point-vice-versa-tangent-plane.jpg)
Differential geometry - Curvature, Surfaces, Manifolds
![dg.differential geometry - Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature - MathOverflow](https://i.ytimg.com/vi/8YCfx4hN-7Q/hq720.jpg?sqp=-oaymwEhCK4FEIIDSFryq4qpAxMIARUAAAAAGAElAADIQj0AgKJD&rs=AOn4CLDwh315lXH-W8KdIRl5gv9dxsYpFA)
Lecture 15: Curvature of Surfaces (Discrete Differential Geometry
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