Minkowski space time is defined in terms of a flat pseudo-Riemannian manifold. I have wondered if it can be redefined as Riamannian manifold and in the case what type of curvature would there appear. ...
We know from MTW  and Synge  how, for participants who were (pairwise) rigid to each other, it may be determined whether or not they were straight to each other, plane to each other, or ...
Let's say point $P$ is the center of mass of an irregularly shaped object. If I make a straight cut trough point $P$ and split the object in two, is it possible for the two pieces to have the same ...
I am currently a high school student interested in a research career in physics. I have self taught myself single variable calculus and elementary physics upto the level of IPHO . And I am comfortable ...
Consider the metric space $(M, d \,)$ where set $M$ contains sufficiently many (at least five) distinct elements, and consider the assignment $c_f$ of coordinates to (the elements of) set $M$, $c_f ...
I have been wondering about some of the different uses of Generalized Complex Geometry (GCG) in Physics. Without going into mathematical detail (see Gualtieri's thesis for reference), a Generalized ...
The wave equation is often written in the form $$(\partial^2_t-\Delta)u=0,$$ involving the Laplace-Beltrami operator $\Delta$. However, the Laplace-Beltrami operator $\Delta$ is defined only in the ...
Why was the truncated icosahedron (i.e. soccer ball) geometry chosen for the implosive lenses in the “Fat Man” atomic bomb?
Quoting from Wolfram Mathworld: " It is the shape used in the construction of soccer balls, and it was also the configuration of the lenses used for focusing the explosive shock waves of the ...
It is known that in F-theory compactifications on CY 4-folds one can get gauge groups with very large ranks. The largest single factor* gauge group for compact CY 4-folds I found in the literature is ...
Let $X$ be a manifold with $G_2$ holonomy and $\Phi$ be the fundamental associative 3-form on $X$. Let $*\Phi$ be the dual co-associative 4-form on $X$. Now consider a particular associative 3-cycle ...