Math_QED : you can show it without Riemannian structure (in fact you can show the assertions above are equivalent to "##M## is homeomorph to a closed set of ##L^{2}(\mathbb{N})##").End of digression.
Hello, to answer to the first question, if you've got a topological space ##M## such that any ##x \in M## admit a neighborhood homeomorph to an open space of ##\mathbb{R}^{n}##, then the following assertion are equivalent :
a)##M## is an Hausdorff space with a countable basis of open...
Their is a a way to developed the formal sum : ##(x_1 + x_2 + ... + x_k)^n## no? It might help but this will create a big sum with a lot of binomial coefficient.
Hello,
If I have a quadratic form ##q## on a ##\mathbb{R}## vectorial space ##E##, its associated bilinear symmetric form ##b## can be deduce by the following formula : ##b(., .) = \frac{q(. + .) - q(.) - q(.)}{2}##. So that, an homogeneous polynomial of degree 2 can be associated to a blinear...
Hi, for the second equality you've got : ##||F(v)||^2 = <v, F(F(v))>## (because ##F## is symmetric) and this equate ##0## since ##v \in Im(F)^{\perp}## and ##F(F(v)) \in Im(F)##. Where is the problem?
Perhaps I didn't understand the question.
Hello, I'm new here. I'm french and I'm very interest at differential geometry. I came here to ask questions and if I can help other people.
My level at school : I achieve (some years ago) a master degree and the agrégation (describtion here : https://en.wikipedia.org/wiki/Agr%C3%A9gation )...