A tensor of type (r,s) on a vector space V is a C-valued function T on V×V×...×V×W×W×...×W (there are r V's and s W's in which W is dual space of V) which is linear in each argument. We take (0, 0) ...
I studied contravariance and covariance concepts in following way: For any vector if we get its components by parallelogram way we achieve contravariant components, and if we want to get its ...
I read somewhere people write gradient in covariant form because of their proposes. I think gradient expanded in covariant basis $i$, $j$, $k$, so by invariance nature of vectors, component of ...
I read the section closed forms and cycles in Arnold's Mathematical Methods of Classical Mechanics (page 196-200), but the problems in this section is too difficult to solve in the way following the ...
Is there a way for calculating the Killing vector fields of a given metric in a quick way? Sure I can guess looking at the metric at the symmetries, and then guess some of them, but, for instance, in ...