List questions from isometry

Published on 19 Feb 2020 - 20:54

958

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Prove that the cone given by $σ(u,v) = (\cos(u)v, \sin(u)v, v)$ with $0 < u < 2\pi$ and $0 < v < \infty$ is isometric to (part of) the plane

Published on 24 Feb 2020 - 15:09

204

Views

Isometry isomorphism between $L_1[0,1]$ and $L_1([0,1]^2)$

Published on 25 Feb 2020 - 4:25

347

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What conditions on an isometric self-map guarantee surjectivity?

Published on 26 Feb 2020 - 16:09

423

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isometry written as a composition of reflections

Published on 25 Mar 2026 - 12:55

200

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What is the significance of isometry.

Published on 28 Feb 2020 - 2:13

50

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Are all bounded linear operators including the ones that are Banach, also isometries?

Published on 25 Mar 2026 - 12:19

980

Views

Simple proof of "Diffeomorphism and distance preserving implies isometry"

Published on 04 Mar 2020 - 0:19

103

Views

Extending an isometry from a hyperplane

Published on 05 Mar 2020 - 6:42

42

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If $A$ is a C*-algebra and $x\in\text{Inv}(A)$ self-adjoint and $\|x\|=\|x^{-1}\|=1$. Is $a\mapsto xax^{-1}$ isometric?

Published on 07 Mar 2020 - 12:29

247

Views

Formula for action of Möbius transformation on the hyperboloid model

Published on 25 Mar 2026 - 20:42

277

Views

Conditions for applying Ito Isometry

Published on 17 Mar 2020 - 10:07

119

Views

How to compute isometry group directly

Published on 18 Mar 2020 - 20:22

158

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Clarification on metric preserving embedding of unit sphere $S^2$

Published on 21 Mar 2020 - 5:31

320

Views

Local isometry on an open subset can be extended

Published on 21 Mar 2020 - 9:17

List Question

All straight curves are geodesics imply Euclidean metric

Prove that the cone given by $σ(u,v) = (\cos(u)v, \sin(u)v, v)$ with $0 < u < 2\pi$ and $0 < v < \infty$ is isometric to (part of) the plane

Isometry isomorphism between $L_1[0,1]$ and $L_1([0,1]^2)$

What conditions on an isometric self-map guarantee surjectivity?

isometry written as a composition of reflections

What is the significance of isometry.

Are all bounded linear operators including the ones that are Banach, also isometries?

Simple proof of "Diffeomorphism and distance preserving implies isometry"

Extending an isometry from a hyperplane

If $A$ is a C*-algebra and $x\in\text{Inv}(A)$ self-adjoint and $\|x\|=\|x^{-1}\|=1$. Is $a\mapsto xax^{-1}$ isometric?

Formula for action of Möbius transformation on the hyperboloid model

Conditions for applying Ito Isometry

How to compute isometry group directly

Clarification on metric preserving embedding of unit sphere $S^2$

Local isometry on an open subset can be extended

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