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Results tagged with quadratic-forms
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user 13972
Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.
21
votes
Accepted
Positive 4-form
(6 October 2023) I'll leave the original argument below because it seems that many people liked it, but, in fact, it wanders around and introduces a lot of unnecessary information, which obscures the …
- 108k
7
votes
Isotropic subvarieties of $ V(x_1^2+\dots+x_n^2-t_1^2-\dots-t_n^2) $
There is a much stronger result: Any irreducible isotropic subvariety of dimension $n$ in $K^{2n}$ (with its split inner product) is an isotropic $n$-plane. No assumption of homogeneity is necessary …
- 108k
7
votes
Accepted
Are constant connection coefficients uniquely determined by the (1,3) curvature coefficients?
It's not hard to see that you don't always have uniqueness up to sign when $n\ge 4$. Just consider the case when $\Gamma^i_{jk}$ is zero except when $i=j=k$. In this case, one has $R^i_{jkl}=0$ for …
- 108k
2
votes
Accepted
if $\Pi_1$ and $\Pi_2$ be elliptic planes then $\Pi_1 \oplus \Pi_2 $ is still elliptic?
No. Note that $V$ has dimension $4$. The maximum dimension of an elliptic subspace of $\Lambda^2(V^\ast)$ is $3$, so if $\Pi_1$ and $\Pi_2$ don't intersect, then $\Pi_1\oplus \Pi_2$ is never ellipti …
- 108k