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Submanifolds Isometric to Euclidean Spaces

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#differential-geometry #riemannian-geometry
1.4k
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On the definition of piecewise differentiable curves

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#derivatives #differential-geometry #manifolds #riemannian-geometry #smooth-manifolds
1.5k
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Hessian of a function at the critical points

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#differential-geometry #riemannian-geometry #morse-theory #hessian-matrix
539
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Is the tangent space to a critical submanifold a subspace of the kernel of the Hessian?

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#differential-geometry #riemannian-geometry #morse-theory #hessian-matrix
184
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What is the connection between information monotonicity and the additivity property of information measures?

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#riemannian-geometry #information-theory #information-geometry
102
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Not all homogeneous manifolds are on the form $G/H$

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#differential-geometry #lie-groups #riemannian-geometry
574
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Checking riemann curvature tensor $C^\infty(M)$ linear in $Z$ with $R(X,Y)Z=\nabla_X\nabla_YZ-\nabla Y\nabla_XZ-\nabla_{[X,Y]}Z$

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#differential-geometry #riemannian-geometry #curvature
880
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Difference between torsion and Lie bracket

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#manifolds #riemannian-geometry #smooth-manifolds #lie-derivative #torsion-groups
3.5k
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Since the Curvature tensor depends on a connection (not metric), is it the relevant quantity to characterize the curvature of Riemannian manifolds?

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#differential-geometry #riemannian-geometry #smooth-manifolds #curvature #affine-geometry
347
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Compactness argument for type I singularities of the mean curvature flow

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#differential-geometry #partial-differential-equations #riemannian-geometry #parabolic-pde #mean-curvature-flows
46
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Riemann Metric of $\mathcal M_1\cup\mathcal M_2$

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#real-analysis #metric-spaces #riemannian-geometry #smooth-manifolds #metric-geometry
92
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How bad can a pole of the derivative of a continuous function be?

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#real-analysis #partial-differential-equations #riemannian-geometry
258
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Constructing a metric with discrete isometries on the sphere

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#riemannian-geometry #projective-space #symmetry #spheres #isometry
1.6k
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$X$ is a Killing field $\iff \langle \nabla_YX,Z \rangle+\langle \nabla _ZX,Y\rangle=0$

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#riemannian-geometry #vector-fields #connections
36
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Computing a twisted version of the energy along a geodesic

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#differential-geometry #riemannian-geometry #smooth-manifolds #geodesic #arc-length

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