Category Archives: Geometry

Geometry, especially curvature and geodesics

Infinite geometry

Posted on 2026/04/24 by arkajad

A week ago I asked Perplexity AI: “Is there a monograph, or a comprehensive review, discussing infinite-dimensional symmetric spaces and Kahler manifolds?” Here is the answer: Yes. There are a few substantial sources on infinite-dimensional symmetric spaces, and many standard … Continue reading →

Posted in Geometry | 12 Comments

Densities

Posted on 2025/12/21 by arkajad

This post introduces “densities”. There is a very nice book, available on arxiv, by Sean M. Carroll: “Lecture Notes on General Relativity“. There, on p. 52, Carroll writes “… we don’t like tensor densities, we like tensors.” Well, I do … Continue reading →

Posted in AI, Geometry, Lorentz transforations, Spin and rotations, Uncategorized | Tagged , , , , , , | 56 Comments

Tensors are geometric objects

Posted on 2025/12/10 by arkajad

Originally, while writing the previous post, I was convinced that this one should be devoted to the Grassmann (or exterior) algebra.  I even began drafting it and managed about half a page before realizing that, if the promise of a … Continue reading →

Posted in Geometry, Uncategorized | Tagged , , , | 16 Comments