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Left-invariant and almost right-invariant metric on a Lie group

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#abstract-algebra #metric-spaces #lie-groups #riemannian-geometry #topological-groups
144
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Does any pseudo-Riemannian metric admit a metric-compatible linear connection with vanishing curvature?

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#differential-geometry #riemannian-geometry
125
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Deriving Levi-Civita Connection on the Space of Compatible Complex Structures

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#riemannian-geometry #complex-geometry #symplectic-geometry
60
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One question about 3 Flat manifold

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#differential-geometry #riemannian-geometry
173
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Given two sets diffeomorphic to the unit ball, are the connected components also diffeomorphic to the unit ball?

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#differential-geometry #riemannian-geometry #smooth-manifolds
173
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Paraboloid is isotropic at only one point

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#differential-geometry #riemannian-geometry #surfaces #curvature
189
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Consequences of Hopf-Rinow Theorem

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#riemannian-geometry
151
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Exercise on conformal metrics

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#riemannian-geometry
227
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Ricci flow diffeomorphism invariance and evolution of curvature using Uhlenbeck's trick

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#differential-geometry #riemannian-geometry #ricci-flow
1.4k
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Riemannian 1-manifold is flat

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#differential-geometry #manifolds #riemannian-geometry
284
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Does there exist an affine connection is not a Riemannian connection?

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#differential-geometry #riemannian-geometry #connections
255
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Characterization of gradient field in Riemannian Geometry

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#differential-geometry #definition #riemannian-geometry #vector-fields
373
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Computing Lie bracket and Levi-Civita connection on Torus

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#differential-geometry #riemannian-geometry #vector-fields #lie-derivative
181
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does the curvature fixes a connection on the principal bundle?

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#differential-geometry #riemannian-geometry #principal-bundles
181
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Discrete and cocompact subgroups of isometries of $\mathbb{R}^n$

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#group-theory #differential-geometry #riemannian-geometry #isometry

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