Let $(M^2,g,\boldsymbol{\xi})$ be a two-dimensional Riemannian manifold endowed with a Riemannian metric $g$ (strictly positive signature) and a Killing field $\boldsymbol{\xi}$. Will there be an isometric embedding into $\mathbb{R}^3$ such that it is symmetric under rotations about some straight line ?
2026-04-04 17:52:55.1775325175
Does any symmetric surface look like a surface of revolution?
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