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Compute a parallel transport

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#differential-geometry #manifolds #riemannian-geometry
649
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Sum of Killing vector fields is a Killing vector field

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#differential-geometry #riemannian-geometry
1.8k
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Is there a better way to show the intrinsic curvature of a cylinder is zero?

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#differential-geometry #riemannian-geometry
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Hessian of a function on Riemannian manifolds

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#differential-geometry #riemannian-geometry
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Pullback of a differential form

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#calculus #geometry #differential-geometry #riemannian-geometry
471
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Clarification of definition of tensor product

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#linear-algebra #riemannian-geometry #tensor-products
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Why is the trace of the Riemann curvature tensor useful?

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#riemannian-geometry
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existence of affine connection on manifold

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#riemannian-geometry #connections
1.6k
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Proof in Hamilton: Divergence theorem for differential forms?

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#integration #differential-geometry #riemannian-geometry #tensors #smooth-manifolds
105
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Can I argue like this to prove that the determinant is positive?

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#differential-geometry #riemannian-geometry
2.1k
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Do we write a metric tensor as a matrix?

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#matrices #riemannian-geometry #tensors
94
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How to prove that volume forms agree on $U_\alpha \cap U_\beta$?

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#differential-geometry #manifolds #riemannian-geometry
827
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Check Christoffel symbol defines Levi-Civita connection

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#riemannian-geometry #connections
64
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Does there exists known special cases of a zero Riemann tensor for 3D metrics?

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#differential-geometry #riemannian-geometry #tensors #conformal-geometry #dimensional-analysis
436
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Question about curvature calculation method in Lee's *Riemannian Manifolds* book

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#riemannian-geometry

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