List questions from riemannian-geometry

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principal curvature in high dimensions

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Are images of isometries of the plane under regular parametrizations of the cylinder themselves isometries of the cylinder?

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Construction G-Invariant Riemannian Metric

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$\mathbf{H}(3)$ is diffeomorphic to $\mathbf{SL}\left( 2,\mathbf{C}\right) \mathbf{/SU}\left( 2\right) $

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Closed geodesic on a Riemannian manifold is homotopic to a closed curve of strictly shorter length

Published on 22 Aug 2018 - 0:56

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$X$ is an admissible variation of $\mathbf{x}$

Published on 25 Mar 2026 - 3:20

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Can we extend any flat metric on the torus to a "standard" global flat metric?

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Understand definition of First Order Frame Field

Published on 25 Aug 2018 - 15:55

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Show that $E_{t}=\left( \mathbf{x}_{t},\mathbf{E}_{1},\mathbf{E}_{2},\mathbf{E}_{3}\right)$ is a first order frame field along $\mathbf{x}_{t}$

Published on 25 Mar 2026 - 21:46

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Textbooks on differential geometry

Published on 26 Aug 2018 - 4:20

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Showing that the Lie bracket of two Killing fields on a Riemannian manifold is again a Killing field using the Killing equation

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Evaluate integral (Chern article)

Published on 27 Aug 2018 - 12:32

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Principal curvatures of surface of revolution

Published on 27 Aug 2018 - 17:34

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The Taylor expansion of a metric: a natural viewpoint?

Published on 27 Aug 2018 - 22:02

List Question

Homogeneous Space of Hyperbolic Space

principal curvature in high dimensions

Are images of isometries of the plane under regular parametrizations of the cylinder themselves isometries of the cylinder?

Construction G-Invariant Riemannian Metric

$\mathbf{H}(3)$ is diffeomorphic to $\mathbf{SL}\left( 2,\mathbf{C}\right) \mathbf{/SU}\left( 2\right) $

Closed geodesic on a Riemannian manifold is homotopic to a closed curve of strictly shorter length

$X$ is an admissible variation of $\mathbf{x}$

Can we extend any flat metric on the torus to a "standard" global flat metric?

Understand definition of First Order Frame Field

Show that $E_{t}=\left( \mathbf{x}_{t},\mathbf{E}_{1},\mathbf{E}_{2},\mathbf{E}_{3}\right)$ is a first order frame field along $\mathbf{x}_{t}$

Textbooks on differential geometry

Showing that the Lie bracket of two Killing fields on a Riemannian manifold is again a Killing field using the Killing equation

Evaluate integral (Chern article)

Principal curvatures of surface of revolution

The Taylor expansion of a metric: a natural viewpoint?

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