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Oct
16 |
answered | A question about curvature for linear connections |
Oct
10 |
comment |
Tori in three-space
Yes. You can make non-geodesic elastic curves in the 2-sphere which oscillate around a great circle. They have enclosed area which is equal to the area of the hemisphere, but the lenght is strictly greater than the lenght of the great circle. Thus, Pinkall's formula for the conformal type implies, that you obtain a rhombic, non-square torus. The existence of these elastic curves follows from theorem 3 in arxiv.1303.1445. |
Sep
30 |
comment |
Equivalence of Harmonic Maps and Conformal Maps on Genus-0 closed surfaces
Dear Skrodde, you are welcome. |
Sep
28 |
answered | compact almost complex submanifolds of complex Lie groups |
Sep
28 |
revised |
Tangent fields spanning the distribution of principal directions on a surface
deleted 11 characters in body |
Sep
28 |
answered | Tangent fields spanning the distribution of principal directions on a surface |
Sep
25 |
revised |
Are the Sasaki metrics on tangent and cotangent bundle isomorphic?
edited body |
Sep
25 |
answered | Are the Sasaki metrics on tangent and cotangent bundle isomorphic? |
Sep
23 |
awarded | Enlightened |
Sep
23 |
awarded | Nice Answer |
Sep
18 |
answered | Equivalence of Harmonic Maps and Conformal Maps on Genus-0 closed surfaces |
Jul
10 |
comment |
Prove that the holonomies along any two homotopic paths are the same if the curvature of the connection vanishes
Dear QIAOJIAXIN, your question is not research level, and you should be able to extract the answer from any differential geometry book dealing with the Frobenius theorem, e.g. Lee's "Manifolds and Differential Geometry". |
Jul
10 |
comment |
Prove that the holonomies along any two homotopic paths are the same if the curvature of the connection vanishes
Dear Dimitri, I think this is not only too complicated, but also circular in the following sense: In order to prove Theorem 4.4. and Lemma 4.5 you have (at some point) to prove a (stronger) version of the assertion, see for example Proposition 3.8 in the mentioned paper. |
Jul
1 |
comment |
Can every hyperelliptic genus 3 surface be minimally immersed in flat $T^3$
Dear Piojo, I do not understand your comment. Whenever you have a minimal surface with translational periods only, you get two holomorphic spinors, and vice versa. The problem is to find two spinors such that the corresponding real parts of the 2g many $\mathbb C^3$ valued periods span a lattice in euclidean 3-space. |
Jul
1 |
revised |
Can every hyperelliptic genus 3 surface be minimally immersed in flat $T^3$
added 16 characters in body |
Jul
1 |
answered | Can every hyperelliptic genus 3 surface be minimally immersed in flat $T^3$ |
Apr
30 |
accepted | Periods of translation surfaces |
Apr
30 |
comment |
Periods of translation surfaces
Dear Matheus, somehow, I have not realized that my question was answered until now. Thanks. |
Mar
12 |
awarded | Yearling |
Dec
12 |
answered | Moduli spaces of connections as representation spaces |