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Does $\nabla g=\omega(\cdot) g$ imply $\nabla$ is metric w.r.t a conformal rescaling of $g$?

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#riemannian-geometry #examples-counterexamples #vector-bundles #conformal-geometry #connections
287
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Isometry group of a lorentzian metric which preserves a Riemannian metric

Published on
#differential-geometry #riemannian-geometry #semi-riemannian-geometry
65
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Can we 'build' spinor structure not only from a Riemann Manifold but 'extract it' also from another algebraic structures?

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#riemannian-geometry #spin-geometry
214
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How to derive the geodesic equations, via Euler Lagrange, from $L=\frac12 g_{ij}\dot x^i\dot x^j$?

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#riemannian-geometry #partial-derivative #geodesic #euler-lagrange-equation
145
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Surface covered by hyperbolic plane admits a hyperbolic metric

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#riemannian-geometry #surfaces #riemann-surfaces #hyperbolic-geometry #covering-spaces
31
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How would the chart around a point vary be different to the tangent space at the same point?

Published on
#manifolds #riemannian-geometry
50
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how we can add a 2-tensor to a 1-form?

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#differential-geometry #metric-spaces #riemannian-geometry
86
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Definition of the surface measure in some Book

Published on
#integration #measure-theory #reference-request #riemannian-geometry
78
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Isometries of a surface with metric of curvature $-1$

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#differential-geometry #riemannian-geometry #hyperbolic-geometry
481
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Inner product on the Hyperbolic half plane

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#metric-spaces #riemannian-geometry #hyperbolic-geometry
651
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Computing volume of Riemannian manifolds and its $n$-sheeted covering

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#differential-geometry #riemannian-geometry #volume #covering-spaces #isometry
58
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Is this a correct definition of a Riemannian metric tensor?

Published on
#riemannian-geometry #curvilinear-coordinates
690
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Definition of closed surface/manifold

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#differential-geometry #manifolds #definition #riemannian-geometry #surfaces
417
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Tangent vector field to a smooth curve over a smooth manifold

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#differential-geometry #vector-spaces #vectors #riemannian-geometry
175
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Soft question: why define smooth manifolds intrinsically?

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#general-topology #differential-geometry #riemannian-geometry #smooth-manifolds

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