# Questions tagged [differential-geometry]

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### How to calculate scalar curvature, Ricci tensor and Christoffel symbols in Mathematica?

I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. Sometimes,...
13k views

### Differential geometry add-ons for Mathematica

I need a differential geometry tool for Mathematica. Is there any add-on? Unfortunately, Mathematica does not include such functionality or I can not find it.
3k views

### How to estimate geodesics on discrete surfaces?

Continuing with my interest on curvature of discrete surfaces here and here, I would like to also calculate and plot geodesics on discretised (triangulated) surfaces. Basically, my long-term idea ...
2k views

### How to speed up estimation of Mean and Gaussian curvatures on triangular meshes?

I am trying to estimate curvatures on a triangulated surface/manifold using the algorithm of : Meyer, M., Desbrun, M., Schröder, P., & Barr, A. H. (2003). Discrete differential-geometry operators ...
3k views

### Compute covariant derivative in Mathematica

I need to compute covariant derivatives in Mathematica. Searching online I just found the package "Ricci" which only does symbolic computations: I instead need to do actual computations. This is ...
1k views

### Visualization of Gaussian Curvature

I need to visualize Gaussian Curvature of a parametric surface. There is a solution in this math.SE post. However, I'm not sure its working because when I draw a sphere it's all white, but it should ...
3k views

### Estimating Principal Curvature Directions on Discrete Surfaces

I am continuing with working on implementing curvature estimations on triangulated surfaces (See: here), using the algorithm of : Meyer, M., Desbrun, M., Schröder, P., & Barr, A. H. (2003). ...
5k views

### Computing Gaussian curvature

Can Gaussian curvature $K$ be computed from WolframAlpha or any other available Mathematica program? Please indicate the program or its reference. If input ...
1k views

### The time-like geodesics (orbits) in the Schwarzschild spacetime

I am trying to plot Schwarzschild's orbit without invoking the geodesic equation. As a reference I am using Chandrasekhar's Book (The Mathematical theory of Black Holes, Oxford University Press). In ...
2k views

### Geodesics on a torus

Is it possible to draw geodesics between the points in a path on a torus - toroidal surface? geodesics: generalization of the notion of a "straight line" to "curved spaces" ...
370 views

149 views

### Constructing a 2D curve from a curvature function dynamically

I want to plot a curve starting from its curvature function and some initial conditions. This code generates a 2D curve with a given curvature (fun) and some initial conditions: ...
157 views

### Calculate surface normals at the boundary of a Graphics3D object

How do I go about calculating and plotting the surface normals at the boundary of a Graphics3D object? For example, consider this custom-defined ...