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Is $\left|\frac{\det(A_{\mu\nu})}{\det(B_{\mu\nu})}\right|$ an invariant for two tensors $A_{\mu\nu}$ and $B_{\mu\nu}$ in a manifold?

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#differential-geometry #manifolds
98
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Connection laplacian and abstract index notation

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#differential-geometry #manifolds #riemannian-geometry #tensors #laplacian
67
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A chart for a finite set

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#differential-geometry #metric-spaces #manifolds #riemannian-geometry #compactness
123
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Every topological manifold admits a countable, locally finite cover by precompact open sets

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#general-topology #analysis #manifolds
37
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Proof request: Trajectories in the stable manifold of a non-hyperbolic fixed point converge to the fixed point

Published on
#reference-request #manifolds #dynamical-systems
99
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Is $D^2\times S^1$ compact?

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#algebraic-topology #manifolds #homology-cohomology
136
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Tangent vectors as differential operators vs equivalence classes of curve in manifold

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#manifolds #tangent-spaces
148
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Change of coordinates on a manifold

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#analysis #differential-geometry #manifolds
900
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Geometric meaning of the rising and the lowering of indices

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#linear-algebra #vectors #manifolds #tensors #differential-forms
88
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Interpretation of basis of tangent space

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#differential-geometry #manifolds #riemannian-geometry #tangent-spaces
52
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Non-escaping property of stable manifold for flows

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#ordinary-differential-equations #manifolds #dynamical-systems #stability-theory
70
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Let $f:\mathbb{R}^m\to\mathbb{R}^n$ be continuous and $M\subseteq \mathbb{R}^m$ be an $m$-manifold. Is the graph of $f$ an $m$-manifold?

Published on
#manifolds #manifolds-with-boundary
111
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Adjoint functors in analysis on manifolds

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#differential-geometry #category-theory #manifolds #smooth-manifolds
62
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Commutativity relation on forms

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#calculus #multivariable-calculus #differential-geometry #manifolds #differential-forms
89
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A different (more intuitive?) definition of the tangent space and the differential. Why are they not used?

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#differential-geometry #manifolds #definition #smooth-manifolds #differential

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