Koeneuze
Reputation
Next privilege 250 Rep.
 Jun13 asked Proof of Hopf's theorem using Liouville May16 comment Euclidean distance on R and Q To solve iii), including rays in the definition of open intervals is unnecessary. A ray of one of those forms can easily be written as a countable union of open intervals, e.g. $(a,\infty) = (a,a+2) \cup (a+1,a+3) \cup ....$ May16 awarded Informed May16 comment Projection of surfaces in $\mathbb{C}^2, \mathbb{C}P^2, \mathbb{C}H^2$ to $\mathbb{R}^3$ 2-dimensional complex hyperbolic space May16 asked Projection of surfaces in $\mathbb{C}^2, \mathbb{C}P^2, \mathbb{C}H^2$ to $\mathbb{R}^3$ Jul2 awarded Curious Jun9 accepted Real part of integral over holomorphic 1-form is zero implies the one-form is zero Jun9 asked Real part of integral over holomorphic 1-form is zero implies the one-form is zero Jun7 awarded Critic Jun3 comment Almost complex structure compatible with Levi-Civita connection of immersed submanifold? Ah, of course, that makes sense, $\nabla$ would not be defined on $(T_pM)^\perp$. However, $\nabla_X Y \in TM$ so $\langle \nabla_XY,JZ\rangle = 0$, exactly because $\nabla_XY$ lies in $TM$, I think? Then that should in fact be enough to prove the theorem I want, with the added condition that $M$ is totally real. Jun3 comment Almost complex structure compatible with Levi-Civita connection of immersed submanifold? I'm quite a beginner in Riemannian Geometry, so I hope you don't mind any stupid questions, but... does TM have to be J-invariant for this question to make sense? The particular case I really need (though I'm interested in the more general statement) is if $M$ is totally real, minimal and of constant seciontal curvature, and $\tilde{M}$ is a complex space form, then $\langle Jh(X,Y),Z \rangle = \langle Jh(X,Z),Y\rangle$ with $h$ the second fundamental form of the immersion. What I stated in the question is (according to my calculations) sufficient to prove this. Jun3 asked Almost complex structure compatible with Levi-Civita connection of immersed submanifold? May29 comment Two doors, 2 guards logic problem (“is XOR a hypothetical statement?”) I see, thank you for the clarification... The "A or B, but if A, ..." is exactly what made me doubt whether XOR was allowed or not. I'm toying with the idea of rephrasing the question by "Is exactly one of the following statements true: '...' and '...'?" which should highlight the non-hypothetical nature of the question? May29 accepted Two doors, 2 guards logic problem (“is XOR a hypothetical statement?”) May29 asked Two doors, 2 guards logic problem (“is XOR a hypothetical statement?”) Oct21 awarded Commentator Oct21 comment Condition so that coefficients nilpotent implies power series nilpotent for non-noetherian ring $R$ with char$(R) = 0$ Sorry, I should've specified that I was looking for a necessary and sufficient condition - I'm looking to describe "what the nilpotent elements of R[[X]] look like", so to speak. Theorem 2 gives a sufficient but not necessary condition, and I believe Corollary 1 does too (where the sufficient but not necessary part is that $A_f$ has to be finitely generated). Oct21 revised Condition so that coefficients nilpotent implies power series nilpotent for non-noetherian ring $R$ with char$(R) = 0$ added 94 characters in body Oct20 comment Condition so that coefficients nilpotent implies power series nilpotent for non-noetherian ring $R$ with char$(R) = 0$ @MartinBrandenburg I had already read the first one, which confirmed the things I mentioned in my post but didn't answer the question. I've just read the second one, but again it only confirms my post (unless I misread something). Oct20 asked Condition so that coefficients nilpotent implies power series nilpotent for non-noetherian ring $R$ with char$(R) = 0$