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The first chern class of $O(1)$ is positive

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#differential-geometry #complex-geometry #curvature #almost-complex
45
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What constraints can be imposed to a variational problem to render a surface with a given curvature?

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#differential-geometry #calculus-of-variations #curvature #euler-lagrange-equation
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
493
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Why is the integral of the unit tangent vector equal to the position vector?

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#vector-analysis #circles #curvature
327
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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
73
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Symmetric tensor of two different vector spaces

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#riemannian-geometry #tensor-products #curvature #ricci-flow
184
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Proof for Cauchy's Definition of Centre of Curvature.

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#differential-geometry #curvature
184
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Canonical connection form on 2-dim surface and Gaussian Curvature

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#differential-geometry #riemannian-geometry #curvature
3.4k
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Finding curvature for $y = \sin ( -2x )$ at $x =\pi/4$

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#calculus #curves #curvature
150
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Riemann curvature tensor

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#differential-geometry #riemannian-geometry #curvature
193
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How can I exploit this definition to proof that spherical surfaces aren't flat?

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#surfaces #curvature
13.6k
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point of maximal curvature on $y=\ln x$

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#calculus #curvature
70
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Prove a curvature identity

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#curvature
346
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surface gradient of the unit normal vector

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#differential-geometry #tensors #curvature

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