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If $M$ is a surface on $\mathbb{R}^3$ then $\frac{D}{dt}V = \frac{d}{dt}V?$

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#differential-geometry #riemannian-geometry
992
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How can I argue that Lie derivative is not a connection?

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#riemannian-geometry
55
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Reference request on a topic on hyperbolic space

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#differential-geometry #reference-request #riemannian-geometry #book-recommendation #hyperbolic-geometry
410
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Inner product on tangent space of projective space

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#riemannian-geometry #inner-products #projective-space
85
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Example of a $C^{1,1}$ surface with constant Gaussian curvate equal to 1, which is not a sphere?

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#differential-geometry #riemannian-geometry #surfaces #curvature
177
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What is the most general setting in which the Einstein convention is relevant?

Published on
#soft-question #terminology #riemannian-geometry #mathematical-physics #tensors
888
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Optimization on a Riemannian manifold

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#differential-geometry #optimization #riemannian-geometry #maxima-minima
30
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Geometric/Topologic Tables Bibliography

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#general-topology #differential-geometry #metric-spaces #differential-topology #riemannian-geometry
15k
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Why isn't there a contravariant derivative? (Or why are all derivatives covariant?)

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#differential-geometry #derivatives #riemannian-geometry #tensors
379
Views

If $f:M\to \bar{M}$ is an immersion, $\bar{M}$ riemannian with Levi-Civita connection $\bar{\nabla}$ then ${\bar{\nabla}}^\perp$ is riemannian on $M$

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#riemannian-geometry
97
Views

Can we realize a distance minimizer via converging sequences?

Published on
#metric-spaces #riemannian-geometry #metric-geometry
83
Views

Riemannian curvature tensor and Schwarz theorem

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#multivariable-calculus #riemannian-geometry
195
Views

Unparametrized lightlike geodesics are invariant under conformal change. How does the parametrization change?

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#riemannian-geometry #conformal-geometry #geodesic #semi-riemannian-geometry
58
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Monotonicity of rank of Ricci tensor under Ricci flow

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#differential-geometry #partial-differential-equations #riemannian-geometry #curvature #ricci-flow
108
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$(M,g,\nabla)$ Riemannian, $f:M\to\mathbb{R}$ then $g(\nabla_{\nabla f}\nabla f,\nabla f) = 0 \Rightarrow \nabla_{\nabla f}{\nabla f} = 0$

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#riemannian-geometry

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