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15
412
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In the proof of Cartan's structure equation

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#differential-geometry #riemannian-geometry #exterior-algebra
369
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Is Gauss map a diffeomorphism onto its image in this case?

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#riemannian-geometry #smooth-manifolds #surfaces #curvature #diffeomorphism
108
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Riemannian norm with respect to the exponential map

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#differential-geometry #riemannian-geometry #calculus-of-variations #vector-fields
506
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"Pedantic" derivation of geodesic equation using pullback bundles

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#differential-geometry #riemannian-geometry #vector-bundles #geodesic #connections
627
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Derivative of Gauss map is the second fundamental form

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#differential-geometry #riemannian-geometry #grassmannian
220
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Embedding whole flat 2-Torus in $\Bbb R^3$

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#differential-geometry #metric-spaces #riemannian-geometry
269
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Differential of gradient on submanifold of Euclidean space

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#differential-geometry #riemannian-geometry #submanifold
245
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Existence of minimizer of energy

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#reference-request #riemannian-geometry #smooth-manifolds #calculus-of-variations #harmonic-functions
95
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Busemann function-like function in Riemannian manifold $\mathbb{R}^n$ is $1$-Lipschitz

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#riemannian-geometry #metric-geometry
328
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Curvature of connection in tautological line bundle

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#differential-geometry #riemannian-geometry #complex-geometry #curvature #projective-space
85
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Differential of a canonical map

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#differential-geometry #riemannian-geometry #curvature #grassmannian #tangent-bundle
1k
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Gradient and laplacian of a function defined on Riemannian manifold in local coordinates.

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#riemannian-geometry #smooth-manifolds #laplacian
816
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Divergence of a vector field on a riemannian manifold

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#solution-verification #riemannian-geometry #smooth-manifolds
55
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Combinations similar to sectional curvature

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#differential-geometry #riemannian-geometry
108
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Read off from second fundamental form if submanifold is contained in a larger totally geodesic submanifold?

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#differential-geometry #riemannian-geometry #submanifold

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