# Questions tagged [differential-geometry]

The tag has no usage guidance.

170 questions
Filter by
Sorted by
Tagged with
138 views
+100

### Face-based discrete directional derivative on triangular mesh

For a scalar function $f$ defined on the faces of a triangulated surface $M$, and a vector field $\mathbf{F}$ on its tangent space, is there a built-in or simple way to get the derivative of $f$ in ...
1 vote
46 views

### Calculate and transfrom the metric to the orthonormal frame

Let's suppose, the line element is like this: $$ds^2 = -a^2(1+2\psi)d\tau^2 - 2a^2 B_idx^i d\tau + a^2(1-2\phi)(dx^2 + dy^2 + dz^2)$$ I like to get the output of the metric components from it, ...
• 149
1 vote
39 views

### Package for calculating ADM mass for a given asymptotically flat metric tensor

I am asking for Mathematica package, such that for the input of an asymptotically flat Lorentzian metric tensor $g_{\mu\nu}$ it will give the ADM mass of the object that creates the corresponding ...
1 vote
84 views

### How to calculate Christoffel symbols and curvature for the Alcubierre metric

I am trying to calculate the the christoffel symbols and a few other quantities for the following metric using the code from https://web.physics.ucsb.edu/~gravitybook/mathematica.html Using the code ...
• 111
51 views

### performance of the NDEigensystem and DEigensystem

I can't find any result and I can't understand what is going wrong. Any help please? My code is: ...
62 views

• 117
238 views

### Plotting / Animating a test planet around a star

I am trying to plot/animate the motion of a test planet around a star using Mathematica in the framework of general relativity. In fact, I want to see the perihelion shift. I am using as inspiration ...
• 165
1 vote
96 views

### Calculating the orthonormal frame of a metric in Mathematica

Let us have a given a general metric (like say Kerr metric) of which I want to find the orthonormal coordinates by developing a general code in Mathematica. One of the reliable method to do this (by ...
• 175
338 views

### How to use MMA to solve the minimal surface?

There is a great old post, but since MMA greatly improves the ability of solving differential equations, especially the Region can be used to define the range of variables. So I ask it again. As the ...
• 26.9k
128 views

### How to get the normal vector of a planar curve pointing "outside" (its circle of curvature)?

I have the following implicit function, for which I need to pick up a point $(x0, y0)$ on it and determine the expression of its normal vector pointing outside. "Outside" here means that the ...
• 735
1 vote
134 views

### TensoriaCalc does not display the correct output

I am trying to use TensoriaCalc to calculate the components of the Ricci and the Riemann tensor of the following metric: $R^{2} \left(d\theta^{2} + \sin^{2}\left(\theta \right)d\phi^{2} \right)$; ...
• 113
1 vote
72 views

### Vector Potential Function of Vector Field with DSolve?

(This is a redux of this.) Why doesn't this work? I have a vector field F1 whose div is 0 with a known vector potential function A2, and I try to get DSolve to solve the differential equation for A2 ...
1 vote
82 views

### Integral of (Elementary) Volume Form over Orientable Surface of Genus 2?

Per this post on math.stackexchange.com, I am told it is impossible to find an elementary formula for a coordinate patch covering of the orientable surface of genus 2 (or higher genus) (or the non-...
294 views

### Length of a toroidal helix

For the toroidal helix defined by ...
1 vote
46 views

### Integrate Differential Form with Parameter with DifferentialForms.m?

In this post, it is shown how to integrate a function with parameter(s) and output a function of the parameter(s). I am trying to do something similar with the DifferentialForms.m package. I have ...
165 views

• 2,195
46 views

### Output of expressions unable to have operations be performed on the expression

I am currently trying to use the code linked in the catalog of spacetimes pdf to calculate chirstoffel symbols for a metric which follows as n := 4 ...
• 119
278 views

### Curvature and torsion of this curve

i was trying to get curvature and torsion of curve in mathematica. of this curve ...
497 views

• 119
106 views

I have a matrix in two different bases. Suppose they are called $g_{\mu \nu}$ in one basis and $\eta_{ab}$ in the other basis. If the transformation between the bases is represented by $T_{\mu}^{\text{... 2 votes 1 answer 111 views ### Problem with ArcCurvature When comparing the outputs of ... • 2,788 10 votes 1 answer 433 views ### Shortest distance between two points on a 2D surface I am working on an interesting problem, that consists of trying to compute the shortest distance between two points on a 2D surface. This 2D surface can be represented in a 3D space by the function$f(...
• 449
Let $g\in\mathcal R^{3\times 3}$ be a given known rank 2 tensor function, $gInv$ its inverse, and $dg\in\mathcal R^{3\times 3\times 3}$ its gradiant: ...