Let $Q$ be a smooth manifold, and let $G$ be a Lie group which acts smoothly on $Q$ on the left. Question 1: does the group $G$ act naturally on the tangent bundle $TQ \to Q$? My motivation here ...
I would like to know what are the applications of the theory of $n$-dimensional crystallographic groups (aka space groups) 1) in mathematics 2) outside of mathematics, besides the applications to ...
This is related to this MO question (and others as well). Hoping that this will not turn out to be too broad, I would like to know about the 'state of the art' of: 1) The problem of classifying ...
I've been asked some questions by a friend interested in crystallography, and the following questions (I'm not an expert) came spontaneous to me: 1) Are there two finite subgroups ...
I'm trying to determine the stabilizer of a line in a plane when acted upon by the group of isometries of the plane. Please note that I'm using the notation found in the Wikipedia article on Euclidean ...