Question

In $\Bbb R^3$, If tangent map of F preserves inner product, then F is an isometry?

score 67 · Answer 1 · 2026-05-10 13:51:05

67

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In $\Bbb R^3$, If tangent map of F preserves inner product, then F is an isometry?

Published on 10 May 2026 - 13:51

score 1.3k · Answer 2 · 2026-04-10 23:34:31

1.3k

Views

Composition of a rotation and a traslation is a rotation

Published on 10 Apr 2026 - 23:34

score 55 · Answer 3 · 2026-04-12 00:36:13

55

Views

Identification of the ultraproduct of dual space as subset of the dual of ultraproduct.

Published on 12 Apr 2026 - 0:36

score 62 · Answer 4 · 2026-04-13 21:36:57

62

Views

Can we make a suitable choice of y-axis in proving that any translation or rotation is the product of two reflections?

Published on 13 Apr 2026 - 21:36

score 66 · Answer 5 · 2026-04-15 11:22:10

66

Views

If v and w are orthogonal vectors and their images f(v), f(w) are orthogonal there exists an isometry we can build with a scalar $\alpha$

Published on 15 Apr 2026 - 11:22

score 568 · Answer 6 · 2026-04-14 05:30:48

568

Views

Proving that a map is an isometry.

Published on 14 Apr 2026 - 5:30

score 136 · Answer 7 · 2026-04-15 15:00:30

136

Views

Classifying isometries of $\Bbb{E}^n$

Published on 15 Apr 2026 - 15:00

score 851 · Answer 8 · 2026-04-11 05:30:12

851

Views

Isomorphism and Homeomorphism in Normed Spaces

Published on 11 Apr 2026 - 5:30

score 477 · Answer 9 · 2026-04-12 01:24:26

477

Views

How many "elementary" isometries are needed to generate any isometry of an n-dimensional Euclidean space?

Published on 12 Apr 2026 - 1:24

score 775 · Answer 10 · 2026-04-10 22:58:38

775

Views

Are non-bijective isometries necessarily affine functions?

Published on 10 Apr 2026 - 22:58

score 173 · Answer 11 · 2026-04-17 00:03:42

173

Views

Isometrically embed a pentagon into $\mathbb{R}^2$

Published on 17 Apr 2026 - 0:03

score 129 · Answer 12 · 2026-04-15 17:55:59

129

Views

A map that preserves unit distances is an isometry

Published on 15 Apr 2026 - 17:55

score 141 · Answer 13 · 2026-04-14 20:25:26

141

Views

Isometrically embed $K$-gon into $\mathbb{R}^N$

Published on 14 Apr 2026 - 20:25

score 123 · Answer 14 · 2026-04-09 23:59:21

123

Views

Definition of metric and inner product in diff geo and definition of isometry.

Published on 09 Apr 2026 - 23:59

score 415 · Answer 15 · 2026-04-12 07:19:47

415

Views

Given an open subset of a Riemannian manifold, is the group of isometries that extend to a global isometry closed?

Published on 12 Apr 2026 - 7:19

List Question

In $\Bbb R^3$, If tangent map of F preserves inner product, then F is an isometry?

Composition of a rotation and a traslation is a rotation

Identification of the ultraproduct of dual space as subset of the dual of ultraproduct.

Can we make a suitable choice of y-axis in proving that any translation or rotation is the product of two reflections?

If v and w are orthogonal vectors and their images f(v), f(w) are orthogonal there exists an isometry we can build with a scalar $\alpha$

Proving that a map is an isometry.

Classifying isometries of $\Bbb{E}^n$

Isomorphism and Homeomorphism in Normed Spaces

How many "elementary" isometries are needed to generate any isometry of an n-dimensional Euclidean space?

Are non-bijective isometries necessarily affine functions?

Isometrically embed a pentagon into $\mathbb{R}^2$

A map that preserves unit distances is an isometry

Isometrically embed $K$-gon into $\mathbb{R}^N$

Definition of metric and inner product in diff geo and definition of isometry.

Given an open subset of a Riemannian manifold, is the group of isometries that extend to a global isometry closed?

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