bio | website | |
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location | Stony Brook | |
age | ||
visits | member for | 2 years, 10 months |
seen | 11 hours ago | |
stats | profile views | 216 |
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 |