# A Note on Isometric Embeddings of Surfaces of Revolution

@article{Engman2002ANO, title={A Note on Isometric Embeddings of Surfaces of Revolution}, author={Martin Engman}, journal={The American Mathematical Monthly}, year={2002}, volume={111}, pages={251 - 255} }

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Solutions of the planar Kepler problem with fixed energy h determine geodesics of the corresponding Jacobi–Maupertuis metric. This is a Riemannian metric on ℝ2 if h ⩾ 0 or on a disk D ⊂ ℝ2 if h < 0.…

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Solutions of the planar Kepler problem with fixed energy h determine geodesics of the corresponding Jacobi–Maupertuis metric. This is a Riemannian metric on ℝ2 if h ⩾ 0 or on a disk D ⊂ ℝ2 if h < 0.…

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Under certain conditions, a (1 + 1)-dimensional slice ĝ of a spherically symmetric black hole spacetime can be equivariantly embedded in (2 + 1)-dimensional Minkowski space. The embedding depends on…

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Under certain conditions, a (1 + 1)-dimensional slice ĝ of a spherically symmetric black hole spacetime can be equivariantly embedded in (2 + 1)-dimensional Minkowski space. The embedding depends on…

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Abstract A sharp upper bound on the first ${{S}^{1}}$ invariant eigenvalue of the Laplacian for ${{S}^{1}}$ invariant metrics on ${{S}^{2}}$ is used to find obstructions to the existence of…

### Space–time slices and surfaces of revolution

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Under certain conditions, a (1+1)-dimensional slice ĝ of a spherically symmetric black hole space–time can be equivariantly embedded in (2+1)-dimensional Minkowski space. The embedding depends on a…

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SummaryLetP be a finite set of three or more noncollinear points in the plane. A line which contains two or more points ofP is called aconnecting line (determined byP), and we call a connecting…

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Informally, a surface of revolution is a 2-dimensional Riemannian manifold Σ equipped with an isometric circle action. Surfaces of revolution are among the simplest objects in differential geometry;…

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### The Spectrum and Isometric Embeddings of Surfaces of Revolution

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Abstract A sharp upper bound on the first ${{S}^{1}}$ invariant eigenvalue of the Laplacian for ${{S}^{1}}$ invariant metrics on ${{S}^{2}}$ is used to find obstructions to the existence of…

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If you really want to be smarter, reading can be one of the lots ways to evoke and realize. Many people who like reading will have more knowledge and experiences. Reading can be a way to gain…