User Thomas

14 votes

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Orientability of $m\times n$ matrices with rank $r$

answered Jun 14, 2016 at 9:23

14 votes

Why should we expect the connection between complex arithmetic and geometry?

answered Oct 9, 2020 at 9:45

12 votes

What's true in $\mathbb{R}^4$, false in $\mathbb{R}^3$ and uninteresting in $\mathbb{R}^5$?

answered Jan 11, 2016 at 18:15

11 votes

If $T$ is self-adjoint then $||T^n|| = ||T||^n$

answered May 15, 2021 at 7:06

10 votes

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Can a free product of groups be co-Hopfian?

answered Apr 6, 2022 at 14:26

10 votes

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Levi-Civita-connection of an embedded submanifold is induced by the orthogonal projection of the Levi-Civita-connection of the original manifold

answered Jan 15, 2018 at 11:12

9 votes

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Are complex projective spaces orientable?

answered Aug 25, 2016 at 2:44

8 votes

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Determine with justification, whether $S^2 \times S^4$ is homeomorphic to $\mathbb{C}P^3$.

answered Mar 20, 2020 at 14:59

8 votes

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How come the genus of algebraic curve can be any natural number?

answered Apr 20, 2021 at 4:44

7 votes

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Torsion-free Lie groups

answered Mar 2, 2021 at 9:28

7 votes

Motivation for Kahler Geometry

answered Apr 15, 2020 at 10:26

7 votes

Liouvilles theorem question - show $f$ is constant

answered Apr 6, 2017 at 13:17

6 votes

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Relation between left and right invariant vector fields.

answered Jul 7, 2017 at 4:33

6 votes

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If $T^m$ is a contraction, has $T$ got a fixed point?

answered Feb 19, 2019 at 17:43

6 votes

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How to prove the line exist?

answered Dec 23, 2016 at 14:37

6 votes

Showing that $\mathbb{Z}[i]$ is not isomorphic to $\mathbb{Z}[\sqrt{2}]$

answered Apr 5, 2017 at 16:40

6 votes

"Every geometry is a projective geometry." So is hyperbolic geometry a projective geometry?

answered Oct 29, 2015 at 8:00

5 votes

Which of the following is true for $0 < x < 1$ if $f''(x) - 2f '(x) + f(x) \geq x$ , $x\in [0, 1]$?

answered Nov 5, 2015 at 16:20

5 votes

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Grassmannian, symmetric, idempotent matrices of trace $n$?

answered Dec 20, 2015 at 14:01

5 votes

How to understand conjugate points on a Riemannian manifold?

answered Feb 9, 2016 at 17:17

5 votes

Geodesic in hyperbolic plane

answered Apr 2, 2017 at 5:42

5 votes

Let $S$ be the set of all circles on the unit sphere in $\mathbf{R}^3$. Give a smooth manifold structure to $S$.

answered Jan 30, 2017 at 17:06

5 votes

What is the affine connection, and what is the intuition behind/for affine connection?

answered Feb 17, 2017 at 8:05

5 votes

Grassmanian $(2, 4)$ homeomorphic to $S^2 \times S^2$

answered Jun 17, 2016 at 6:25

5 votes

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The roots of a polynomial are a continuous function of the coefficients

answered Apr 7, 2016 at 7:48

5 votes

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Proof $x^3+ax^2+bx+c-e^x=0$ has at least one solution

answered Jan 1, 2019 at 9:22

5 votes

Constructing a submanifold transversal to a given vector field

answered Jul 7, 2017 at 17:34

5 votes

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Euler Characteristic of fiber bundle using Differential Geometry

answered Jul 1, 2017 at 10:04

5 votes

Accepted

Lie groups having a circle subgroup

answered May 3, 2017 at 5:05

5 votes

Order of the fundamental group from the metric of a Riemannian manifold

answered Jul 18, 2023 at 8:21

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323 Answers

Orientability of $m\times n$ matrices with rank $r$

Why should we expect the connection between complex arithmetic and geometry?

What's true in $\mathbb{R}^4$, false in $\mathbb{R}^3$ and uninteresting in $\mathbb{R}^5$?

If $T$ is self-adjoint then $||T^n|| = ||T||^n$

Can a free product of groups be co-Hopfian?

Levi-Civita-connection of an embedded submanifold is induced by the orthogonal projection of the Levi-Civita-connection of the original manifold

Are complex projective spaces orientable?

Determine with justification, whether $S^2 \times S^4$ is homeomorphic to $\mathbb{C}P^3$.

How come the genus of algebraic curve can be any natural number?

Torsion-free Lie groups

Motivation for Kahler Geometry

Liouvilles theorem question - show $f$ is constant

Relation between left and right invariant vector fields.

If $T^m$ is a contraction, has $T$ got a fixed point?

How to prove the line exist?

Showing that $\mathbb{Z}[i]$ is not isomorphic to $\mathbb{Z}[\sqrt{2}]$

"Every geometry is a projective geometry." So is hyperbolic geometry a projective geometry?

Which of the following is true for $0 < x < 1$ if $f''(x) - 2f '(x) + f(x) \geq x$ , $x\in [0, 1]$?

Grassmannian, symmetric, idempotent matrices of trace $n$?

How to understand conjugate points on a Riemannian manifold?

Geodesic in hyperbolic plane

Let $S$ be the set of all circles on the unit sphere in $\mathbf{R}^3$. Give a smooth manifold structure to $S$.

What is the affine connection, and what is the intuition behind/for affine connection?

Grassmanian $(2, 4)$ homeomorphic to $S^2 \times S^2$

The roots of a polynomial are a continuous function of the coefficients

Proof $x^3+ax^2+bx+c-e^x=0$ has at least one solution

Constructing a submanifold transversal to a given vector field

Euler Characteristic of fiber bundle using Differential Geometry

Lie groups having a circle subgroup

Order of the fundamental group from the metric of a Riemannian manifold