320 reputation
27
bio website
location Stony Brook
age
visits member for 2 years, 10 months
seen 11 hours ago
Studying physics, but very interested in geometry and topology.

Apr
13
comment 3d-analog of “every 2d oriented manifold is complex”
Thanks for replying and the algebra is quite interesting. But as you stated it's not an analog I'm looking for. Hope there will be some other suggestions.
Apr
9
revised 3d-analog of “every 2d oriented manifold is complex”
added 5 characters in body
Apr
9
revised 3d-analog of “every 2d oriented manifold is complex”
added 118 characters in body
Apr
9
asked 3d-analog of “every 2d oriented manifold is complex”
Apr
9
revised a section invariant under Reeb flow
Explain what is meant for a Lie-derivative on a section
Apr
9
revised a section invariant under Reeb flow
Explain what is meant for a Lie-derivative on a section
Apr
9
comment a section invariant under Reeb flow
By $\mathcal{L}_R \sigma = $ I mean the $\mathcal{L} sigma_i = 0$ ,where $\sigma = \sigma_i e_i$ and $e_i$ is local basis for the vector bundle (So $R$ does not act on the basis $e_i$). It's not a coordinate-independent description, more like a "gauge choice". So I should rephrase as: can I choose local basis, such that all coefficients are invariant under $\mathcal{L}_R$? And to me it is very possible to achieve that, but I'm not sure.
Apr
9
revised a section invariant under Reeb flow
added 8 characters in body
Apr
9
revised a section invariant under Reeb flow
added 7 characters in body
Apr
9
asked a section invariant under Reeb flow
Apr
6
accepted contact metric structure on squashed spheres
Apr
2
comment Connection on canonical $\operatorname{Spin}^\mathbb{C}$ spinor bundle on symplectic manifold
The Lemma 4.4 says it wants to prove there is a $A_0$ such that ${\nabla _{\mathbf{A}_0}} u_0 \in \Omega^1(X, K^{-1})$; should it be trying to prove ${\nabla _{\mathbf{A}_0}} u_0 = 0 \in \Omega^1(X, K^{-1}) $?
Apr
2
comment Connection on canonical $\operatorname{Spin}^\mathbb{C}$ spinor bundle on symplectic manifold
Thank you. I came across Lemma 4.4 before but was not able to fully appreciate the importance. I'll try again.
Apr
1
awarded  Yearling
Apr
1
comment Connection on canonical $\operatorname{Spin}^\mathbb{C}$ spinor bundle on symplectic manifold
@abx: Sorry, I forgot to say $M$ is four-dimensional.
Apr
1
revised Connection on canonical $\operatorname{Spin}^\mathbb{C}$ spinor bundle on symplectic manifold
emphasized $M$ is 4-dimensional
Apr
1
comment contact metric structure on squashed spheres
@OldrichSpacil: I'll try your suggestion. It seems a straightforward and guaranteeing way, though a bit more tedious.
Apr
1
comment contact metric structure on squashed spheres
@RichardMontgomery: Yes I can, and I tried. After playing with the expression, I think inserting $\omega_i$ into $\kappa$ or $R$, or $g$, $\Phi$ are equivalent: by rescaling, one can transfer these $\omega_i$ to different quantities while leaving a particular one in standard form. So I think the essential problem is in my anzartz: inserting simple $\omega^{\rm power}_i$ coefficients can not do the job.
Apr
1
asked Connection on canonical $\operatorname{Spin}^\mathbb{C}$ spinor bundle on symplectic manifold
Mar
29
asked contact metric structure on squashed spheres