What is $\nabla X$ in Riemannian geometry?
30032
What does it mean to take the gradient of a vector field?
125774
Derivative of $a^x$ from first principles
42361
Why do we use the Euclidean metric on $\mathbb{R}^2$?
26658
A proof for $\nabla |u|^p = p\ \text{sgn}(u)|u|^{p-1}\nabla u$.
123235
A smooth vector field on $S^2$ vanishing at a single point
46358
geometric interpretation of $\vec v \cdot \operatorname{curl} \vec v = 0 $
21553
Prove that $\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$
63098
Properly discontinuous actions and discrete groups in complete Riemannian manifolds.
48563
If $\Gamma^k_{ij}(p)=0$, then $\nabla_{E_i}E_j (p)=0?$
16463
Is the function $\mbox{tr}(XAX')$ convex?
98800
Do local flows of left-invariant vector fields satisfy $\Phi_X^t\circ L_x=L_x\circ \Phi_X^t$?
109358
Prove the Curvature Tensor is a Tensor
39094
Lie bracket of vector fields on $\Bbb R^{n}$
93314
At what point is the curvature of $y=-\ln(x)$ maximal?
35298
A question about the higher-order Weyl variation for the geodesic distance
66939
Picturing the how the covariant derivative acts on vector fields
26379
What is non-manifold geometry?