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How connection helps us to identify two different vector spaces?

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#differential-geometry #riemannian-geometry #vector-bundles #connections
95
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Formula for covariant derivatives on principal bundles

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#differential-geometry #connections #principal-bundles
162
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Is every compact manifold with a connection geodesically complete?

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#ordinary-differential-equations #differential-geometry #riemannian-geometry #smooth-manifolds #connections
88
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Baby example of a covariant derivative - mistake in Taubes' Differential Geometry?

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#differential-geometry #vector-bundles #connections
132
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Dimension of the stalk of parallel sections and curvature rank

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#differential-geometry #vector-bundles #connections
193
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Is there a proof via Chern-Weil theory that the first Chern numbers of two $\mathbb R$-isomorphic complex vector bundles are equal mod 2?

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#differential-geometry #vector-bundles #connections #characteristic-classes
91
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Do we need gammas to determine $\nabla$?

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#differential-geometry #manifolds #tensors #connections
86
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Positivity of dual Curvature

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#differential-geometry #complex-geometry #vector-bundles #connections
340
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Christoffel symbols, dual space

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#differential-geometry #smooth-manifolds #connections
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
98
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Riemann Manifold equipped with Euclidean metric

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#differential-geometry #manifolds #riemannian-geometry #connections
352
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How do the Christoffel symbols on an abstract manifold relate to those on submanifolds?

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#differential-geometry #connections #submanifold
91
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Katz's proof of Cartier's (descent) theorem

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#algebraic-geometry #proof-explanation #connections #quasicoherent-sheaves #positive-characteristic
91
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Construction of connections given in "From Calculus to Cohomology"

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#differential-geometry #vector-bundles #connections
116
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Invariant connection form

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#differential-geometry #connections #gauge-theory

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