User Matheus Andrade

11 votes

0 answers

194 views

Proving a manifold with certain homogeneous property is Einstein

asked Jun 24, 2021 at 1:20

9 votes

2 answers

264 views

For what metric spaces $(X, d) \ \exists s > 0$ s.t for all $\epsilon < s$ and all $x \in X$, we have $\text{diam}(B_d(x, \epsilon)) = 2\epsilon$?

asked Feb 8, 2019 at 13:28

8 votes

3 answers

2k views

Is there an easy proof that every closed curve is contained in a ball?

asked Sep 10, 2018 at 14:57

8 votes

2 answers

1k views

Calculating the curvature of product manifold $\mathbb{S}^2 \times \mathbb{R}$

asked Sep 18, 2019 at 1:19

6 votes

1 answer

4k views

Proving a few properties of Bertrand curves

asked Feb 19, 2018 at 13:26

5 votes

1 answer

935 views

"Discovering" the hyperbolic functions $\cosh(x)$ and $\sinh(x)$

asked Feb 2, 2018 at 0:51

5 votes

2 answers

324 views

Injectiveness and surjectiveness of $f$ and of $g$, respectively, of the composition $g\circ f$.

asked Mar 31, 2018 at 8:56

5 votes

2 answers

484 views

Proof verification that the sequence $x_n = \frac{1}{n}$ converges to every point of $\mathbb{R}$ on the cofinite topology

asked Jan 13, 2019 at 19:37

5 votes

1 answer

341 views

Norm of Riemannian curvature tensor on an Einstein manifold under the RIcci flow

asked Aug 3, 2021 at 20:50

5 votes

1 answer

581 views

Calculating scalar curvature of a warped product $I \times N^n(k)$

asked Jan 10, 2023 at 22:56

4 votes

1 answer

181 views

Finding a metric of constant negative curvature on cylinder over a torus ($\mathbb{S}^1 \times \mathbb{S}^1 \times \mathbb{R}$)

asked Jun 26, 2021 at 23:04

4 votes

0 answers

168 views

Proving radius of injectivity goes to zero if volume goes to zero

asked Jun 27, 2021 at 21:59

4 votes

0 answers

152 views

Showing that Hopf fibration admits no global sections (not a duplicate!)

asked Nov 23, 2020 at 1:00

4 votes

2 answers

161 views

How can I prove that $\lim_{n \to \infty}\left(1+c\cdot \left(\exp\left(\frac{it}{n}\right) - 1\right)\right)^n=\exp(i\cdot tc)$?

asked May 6, 2021 at 5:15

4 votes

1 answer

646 views

Proof verification that $\overline{\mathbb{R}^{\infty}} = \mathbb{R^\omega}$ and $\overline{\mathbb{R}^{\infty}} = \mathbb{R^\infty}$ in prod/box top.

asked Jan 17, 2019 at 22:30

4 votes

4 answers

83 views

Are there infinitely many pairs $r, s \in \mathbb{Q}$ such that $r + s \neq 0$ and $\frac{1}{r} + \frac{1}{s}$ are both integers?

asked Nov 6, 2018 at 23:13

4 votes

1 answer

201 views

Establishing isomorphisms between polynomial quotient rings

asked May 14, 2019 at 1:15

4 votes

1 answer

2k views

Lie derivative "commutes" with pullback by time dependent diffeomorphisms

asked May 7, 2020 at 6:12

4 votes

2 answers

771 views

Proving that in neutral geometry a line cannot be wholly contained in a triangle

asked Apr 6, 2018 at 20:53

4 votes

2 answers

1k views

Proving that two curves in $\mathbb{R^3}$ with the same binormal vector are congruent

asked Feb 10, 2018 at 0:55

3 votes

0 answers

161 views

Contact order of a space curve with one of it's tangent lines

asked Feb 15, 2018 at 11:15

3 votes

1 answer

50 views

Is there a typo on this remark? Should it be $(\bar u,\bar v)$ instead of $(u,v)$?

asked Feb 22, 2018 at 21:00

3 votes

2 answers

2k views

Describing all plane curves with constant curvature

asked Dec 15, 2017 at 6:12

3 votes

3 answers

278 views

Getting back the original curve having only the curvature

asked Jan 10, 2018 at 15:25

3 votes

1 answer

3k views

How does this definition of the oriented angle differ from the usual (non reflexive angle) one?

asked Mar 13, 2018 at 13:34

3 votes

3 answers

114 views

Proving equality between sets (elementary set theory)

asked Mar 15, 2018 at 0:19

3 votes

1 answer

259 views

How can one generalize the Gauss map to higher dimensions? More specifically, bi-dimensional manifolds in $\mathbb{R}^4$

asked Aug 1, 2018 at 21:16

3 votes

1 answer

109 views

What does the "growing angle of a curve" actually mean?

asked May 24, 2018 at 18:09

3 votes

1 answer

333 views

Using the linearization of scalar curvature operator to obtain the contracted second Bianchi identity

asked Apr 8, 2020 at 23:47

3 votes

1 answer

205 views

Einstein manifolds with metric locally conformal to that of a manifold of constant sectional curvature have constant sectional curvature as well

asked Jun 12, 2019 at 0:39

Stack Exchange Network

216 Questions

Proving a manifold with certain homogeneous property is Einstein

For what metric spaces $(X, d) \ \exists s > 0$ s.t for all $\epsilon < s$ and all $x \in X$, we have $\text{diam}(B_d(x, \epsilon)) = 2\epsilon$?

Is there an easy proof that every closed curve is contained in a ball?

Calculating the curvature of product manifold $\mathbb{S}^2 \times \mathbb{R}$

Proving a few properties of Bertrand curves

"Discovering" the hyperbolic functions $\cosh(x)$ and $\sinh(x)$

Injectiveness and surjectiveness of $f$ and of $g$, respectively, of the composition $g\circ f$.

Proof verification that the sequence $x_n = \frac{1}{n}$ converges to every point of $\mathbb{R}$ on the cofinite topology

Norm of Riemannian curvature tensor on an Einstein manifold under the RIcci flow

Calculating scalar curvature of a warped product $I \times N^n(k)$

Finding a metric of constant negative curvature on cylinder over a torus ($\mathbb{S}^1 \times \mathbb{S}^1 \times \mathbb{R}$)

Proving radius of injectivity goes to zero if volume goes to zero

Showing that Hopf fibration admits no global sections (not a duplicate!)

How can I prove that $\lim_{n \to \infty}\left(1+c\cdot \left(\exp\left(\frac{it}{n}\right) - 1\right)\right)^n=\exp(i\cdot tc)$?

Proof verification that $\overline{\mathbb{R}^{\infty}} = \mathbb{R^\omega}$ and $\overline{\mathbb{R}^{\infty}} = \mathbb{R^\infty}$ in prod/box top.

Are there infinitely many pairs $r, s \in \mathbb{Q}$ such that $r + s \neq 0$ and $\frac{1}{r} + \frac{1}{s}$ are both integers?

Establishing isomorphisms between polynomial quotient rings

Lie derivative "commutes" with pullback by time dependent diffeomorphisms

Proving that in neutral geometry a line cannot be wholly contained in a triangle

Proving that two curves in $\mathbb{R^3}$ with the same binormal vector are congruent

Contact order of a space curve with one of it's tangent lines

Is there a typo on this remark? Should it be $(\bar u,\bar v)$ instead of $(u,v)$?

Describing all plane curves with constant curvature

Getting back the original curve having only the curvature

How does this definition of the oriented angle differ from the usual (non reflexive angle) one?

Proving equality between sets (elementary set theory)

How can one generalize the Gauss map to higher dimensions? More specifically, bi-dimensional manifolds in $\mathbb{R}^4$

What does the "growing angle of a curve" actually mean?

Using the linearization of scalar curvature operator to obtain the contracted second Bianchi identity

Einstein manifolds with metric locally conformal to that of a manifold of constant sectional curvature have constant sectional curvature as well