Question

Show through $\varphi (z) = \frac{z-i}{z+1}$ diffeomorphism $\mathbb{R}^{2}_{+}\longrightarrow U$, defined w.r.t. the hyperbolic metric is an isometry

score 93 · Answer 1 · 2026-03-27 00:10:19

93

Views

Show through $\varphi (z) = \frac{z-i}{z+1}$ diffeomorphism $\mathbb{R}^{2}_{+}\longrightarrow U$, defined w.r.t. the hyperbolic metric is an isometry

Published on 27 Mar 2026 - 0:10

score 74 · Answer 2 · 2021-01-18 17:39:56

74

Views

Isometries of fiber bundles

Published on 18 Jan 2021 - 17:39

score 112 · Answer 3 · 2021-01-18 18:04:00

112

Views

Understanding the isometries of $\widetilde{SL(2,\mathbb{R})}$

Published on 18 Jan 2021 - 18:04

score 99 · Answer 4 · 2021-01-19 01:29:59

99

Views

Isometric linear operators on Hilbert spaces

Published on 19 Jan 2021 - 1:29

score 131 · Answer 5 · 2026-03-27 13:47:22

131

Views

Coxeter: An opposite isometry with no invariant point is a glide reflection. Me: What about a reflection followed by a rotation?

Published on 27 Mar 2026 - 13:47

score 310 · Answer 6 · 2021-01-21 15:12:35

310

Views

Is every subgroup of $\mathrm{Isom}(\mathbb{R}^n)$ a semidirect product $T \rtimes Q$?

Published on 21 Jan 2021 - 15:12

score 37 · Answer 7 · 2021-01-25 14:40:02

37

Views

Finite isometric Hilbert space

Published on 25 Jan 2021 - 14:40

score 81 · Answer 8 · 2021-01-29 11:25:39

81

Views

Generalising parity to infinite groups

Published on 29 Jan 2021 - 11:25

score 187 · Answer 9 · 2021-02-02 19:58:36

187

Views

Isometry group of $N$ using $f:M\to N$ and the isometry group of $M$

Published on 02 Feb 2021 - 19:58

score 48 · Answer 10 · 2021-02-03 16:56:59

48

Views

How do I show this is an isometry relating to First Fundamental Form?

Published on 03 Feb 2021 - 16:56

score 68 · Answer 11 · 2021-02-09 15:16:42

68

Views

How to classify discrete groups of motions

Published on 09 Feb 2021 - 15:16

score 72 · Answer 12 · 2021-02-13 14:49:04

72

Views

isometry group of double torus

Published on 13 Feb 2021 - 14:49

score 36 · Answer 13 · 2026-03-29 16:49:37

36

Views

If $f$ is an isometry between open sets, is $\left|\det{\rm D}f\right|=1$?

Published on 29 Mar 2026 - 16:49

score 227 · Answer 14 · 2021-02-15 18:53:30

227

Views

Every isometry of the Riemannian manifold $(\mathbb{R}^n, g)$ is a composition of a rotation and a translation

Published on 15 Feb 2021 - 18:53

score 135 · Answer 15 · 2021-02-16 08:12:30

135

Views

Isometry for polynomials of degree at most $n$

Published on 16 Feb 2021 - 8:12

List Question

Show through $\varphi (z) = \frac{z-i}{z+1}$ diffeomorphism $\mathbb{R}^{2}_{+}\longrightarrow U$, defined w.r.t. the hyperbolic metric is an isometry

Isometries of fiber bundles

Understanding the isometries of $\widetilde{SL(2,\mathbb{R})}$

Isometric linear operators on Hilbert spaces

Coxeter: An opposite isometry with no invariant point is a glide reflection. Me: What about a reflection followed by a rotation?

Is every subgroup of $\mathrm{Isom}(\mathbb{R}^n)$ a semidirect product $T \rtimes Q$?

Finite isometric Hilbert space

Generalising parity to infinite groups

Isometry group of $N$ using $f:M\to N$ and the isometry group of $M$

How do I show this is an isometry relating to First Fundamental Form?

How to classify discrete groups of motions

isometry group of double torus

If $f$ is an isometry between open sets, is $\left|\det{\rm D}f\right|=1$?

Every isometry of the Riemannian manifold $(\mathbb{R}^n, g)$ is a composition of a rotation and a translation

Isometry for polynomials of degree at most $n$

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