# G_infinity

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bio website location Salerno, Italy age 36 member for 3 years, 5 months seen 10 hours ago profile views 833

Reasonably expert in Differential Geometry, I work mostly with jet bundles and their natural structures trying to exploit them in the areas of nonlinear PDEs and Calculus of Variations.

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 Jul 31 comment What does it mean that the Hessian is proportional to the metric? Very illuminating - thanks! The statement "The level sets of your function formed by manifolds with constant normal curvature" is the most interesting one for me: do you have a reference for it? Jul 31 accepted What does it mean that the Hessian is proportional to the metric? Jul 31 asked What does it mean that the Hessian is proportional to the metric? Jul 30 comment Is there a well-known tautological bundle over $\mathbb{P}(\Lambda^nV)$? Ok, let me try. If $[\omega]\in \mathrm{G}(n,V)$, then $\omega=v_1\wedge\cdots\wedge v_n$, and $\pi^{-1}([\omega])=\langle v_1,\ldots,v_n\rangle$, which is the easy implication. Conversely, knowing that $\dim \pi^{-1}([\omega])=n$, you choose a basis of $V$ such that $\{v_1,\ldots,v_n\}$ generates $\pi^{-1}([\omega])$: now you suggest to write down $\omega$ as a linear combination of $v_1\wedge\cdots\wedge v_n$ and other terms, and show that the coefficients in front of the latter must necessarily be zero. Yes, it should work, thanks! Do you have any clue about question #2? Jul 30 revised Is there a well-known tautological bundle over $\mathbb{P}(\Lambda^nV)$? Removed unnecessary "$\times V$" from the title Jul 29 revised Is there a well-known tautological bundle over $\mathbb{P}(\Lambda^nV)$? I have completely rewritten the question "Is the tautological bundle over the Grassmannian inherited from a bundle over the Plucker embedding space?" since from the users' feedback I realised it was lousily laid down. The content however is unaltered. Jul 25 comment Triangles in rigid Riemann surfaces Now I understand. You are absolutely right. Jul 25 comment Triangles in rigid Riemann surfaces Help me to understand your reasoning. First, by transitivity, you reduce the problem to the case when the two triangles have a vertex in common, say $x_0$: then you are basically asking whether the isotropy subgroup $G_{x_0}$ is 2-transitive (any triangle with one vertex $x_0$ is uniquely determined by two other points). And you say "NO" by using finiteness of $G_{x_0}$: is this enough? What if the surface is the hyperbolic plane: does this finiteness argument works? Jul 21 answered Transformations that leave the Plucker embedding of G(2,4) invariant Jul 14 revised Is there a well-known tautological bundle over $\mathbb{P}(\Lambda^nV)$? Changed "inherited by" in "inherited from" Jul 13 asked Is there a well-known tautological bundle over $\mathbb{P}(\Lambda^nV)$? Jul 7 comment Stability of the Solar System It also depends on the notion of "Solar System": if it comprises "parabolic" objects like comets (and I believe it should), then it is not stable at all. From my point of view, "stable" and "periodic" are interchangeable terms. Besides, how can you predict when/why/where a distant iceberg will decide to dive into the sun? Jul 7 revised Differential operators between modules, $\mathcal{D}_A(M, M)$ necessarily a filtered, almost commutative ring? added 145 characters in body Jul 7 revised Equivalence of “Weyl Algebra” and “Crystalline” definitions of rings of differential operators between modules? I forgot to add a comment on the kind of modules my reasoning works with Jul 7 answered Differential operators between modules, $\mathcal{D}_A(M, M)$ necessarily a filtered, almost commutative ring? Jul 7 answered Equivalence of “Weyl Algebra” and “Crystalline” definitions of rings of differential operators between modules? Jun 17 awarded Good Question Jun 17 revised Why there is a relation among the second-order minors of a symmetric $4\times 4$ matrix? Added a comment to Allen Knutson answer Jun 16 awarded Self-Learner Jun 16 awarded Yearling