How do I prove that the isometries to the unit sphere are the restriction to S^2(1) of the orthogonal lineal applications of R^3?
50731
Isometries of the sphere $\mathbb{S}^{n}$
65888
A counterexample to theorem about orthogonal projection
1760
Limit of the geometric sequence $\{r^n\}$, with $|r| < 1$, is $0$?
158852
If $\{v_1, v_2, v_3\}$ is an orthonormal basis of $\mathbb{R}^3$ and $v = a_1v_1 + a_2v_2 + a_3v_3$, can we have $|a_1| > 3$?
127248
Norm and unit sphere
60514
Isometric  Left Inverse Adjoint
121449
An isomorphism from $GL_{2}(\mathbb{F_{2}})$ to $S_{3}$
53520
Can a conformal map be turned into an isometry?
110472
Existence of a Pivot Point in Euclidean Geometry
39015
Prove the triangle inequality on the sphere $S^2$ in $\mathbb{R}^3$.
96770
Explicit isomorphism between the four dimensional orthogonal Lie algebra and the direct sum of special linear Lie algebras of dimension 3.
6227
Showing diffeomorphism between $S^1 \subset \mathbb{R}^2$ and $\mathbb{RP}^1$
97994
Orthogonality Relations Exercise, Brezis' Book Functional Analysis
69497
Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
95250
Proof a special extension on the isoperimetric theorem
136083
Show that $\sigma\circ\phi : G_1 \to G_3$ is an isomorphism
92599
Prove there generally is no isomorphism between $R[x]/(x^2-a)$ and $R^2$