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On the definition of the Christoffel symbols

Published on
#derivatives #differential-geometry #riemannian-geometry
121
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The riemannian metric of a neighborhood of the boundary of a compact manifold

Published on
#riemannian-geometry #manifolds-with-boundary
139
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what is the geometry picture of Riemann tensor identity $R(X\wedge Y,V\wedge W) = R(V\wedge W, X\wedge Y)$

Published on
#differential-geometry #riemannian-geometry #curvature #general-relativity #geometric-algebras
82
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Local eigenvectors frame of a isometric immersion

Published on
#geometry #differential-geometry #riemannian-geometry
1k
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Christoffel symbols and torsion of the connection

Published on
#differential-geometry #riemannian-geometry #tensors
91
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set with compact closure under isometry

Published on
#metric-spaces #riemannian-geometry
88
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How to prove or disprove that $f(p):=\min\{{\rm sec}(X,Y)\,\,|\,\, X,X\neq Y\in T_pM\},$ is smooth function?

Published on
#differential-geometry #riemannian-geometry
69
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Upper bound on distance between trajectories that share same initial position and velocity

Published on
#metric-spaces #manifolds #riemannian-geometry #geodesic #connections
75
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Compute the Gauss curvature

Published on
#riemannian-geometry #curvature
45
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riemannienne geometry , differential calculus

Published on
#riemannian-geometry
1.7k
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Gaussian curvature of a given metric

Published on
#riemannian-geometry #curvature
244
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Product manifolds and exterior derivative with interior product

Published on
#differential-geometry #riemannian-geometry #differential-forms #exterior-algebra #exterior-derivative
39
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Show that $Z^{\prime }\left( s\right) -2\sqrt{-1}H\left( s\right) Z\left( s\right) -1=0 $

Published on
#ordinary-differential-equations #analysis #differential-geometry #riemannian-geometry
53
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Solve the ode $W^{\prime }\left( s\right) -2iH\left( s\right) W\left( s\right) -1=0$

Published on
#ordinary-differential-equations #analysis #differential-geometry #riemannian-geometry
141
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Exponential of a vector field on a manifold and diffeomorphisms

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#group-theory #manifolds #riemannian-geometry #vector-fields #diffeomorphism

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