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Can we define flat connection on any given smooth manifold?

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#differential-geometry #riemannian-geometry #smooth-manifolds #connections
271
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Covariant derivative in $\mathbb{R}^n$

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#riemannian-geometry #connections
230
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Metric non symmetric connection in the tangent bundle?

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#differential-geometry #riemannian-geometry #connections
408
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How to derive the Christoffel symbols from the embeding view?

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#differential-geometry #riemannian-geometry
77
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Optimizing potential

Published on
#partial-differential-equations #optimization #riemannian-geometry #convex-optimization #poissons-equation
983
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Understanding Energy minimization and poisson equation

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#partial-differential-equations #optimization #riemannian-geometry
188
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Obtaining embedding from geodesic

Published on
#manifolds #riemannian-geometry #smooth-manifolds #metric-geometry
111
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Line in product mainifold

Published on
#differential-geometry #riemannian-geometry #geodesic
174
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Existence of the lift of a curve

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#general-topology #differential-geometry #riemannian-geometry #covering-spaces
104
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Is the subgroup of homotopically trivial isometries a closed subgroup of the isometry group?

Published on
#general-topology #manifolds #lie-groups #riemannian-geometry #homotopy-theory
525
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Formula for Gaussian curvature in terms of unit tangent vector fields?

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#differential-geometry #riemannian-geometry #curvature
13.6k
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Proving the symmetry of the Ricci tensor?

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#riemannian-geometry #tensors #general-relativity
131
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Finding a closed curve $\gamma$ on a Torus such that $\gamma$ is not pseudo-Anosov

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#differential-geometry #riemannian-geometry #riemann-surfaces #geometric-topology #metric-geometry
76
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A $k$-form is thought of as measuring the flux through an infinitesimal k-parallelepiped

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#differential-geometry #riemannian-geometry #differential-forms
498
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Parallel transport for a conformally equivalent metric

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#differential-geometry #riemannian-geometry #conformal-geometry

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