Why is the absolute gradient of the metric tensor $\nabla_{\alpha} g_{\mu \nu} = 0$ in every coordinate system?
112187
Is there a way to see that $ \nabla_\mu g_{\nu \rho} = 0 $ without explicit computation, where $\nabla_\mu$ refers to the covariant derivative?
1162
Why $\{\mathbf{0}\}$ has dimension zero?
14799
How to show that the spherical metric satisfies the triangle inequality?
133465
Stokes and Gauss' Divergence theorem on a closed smooth surface in $\Bbb R^3$
77951
Dirac's delta in 3 dimensions: proof of $\nabla^2(\|\boldsymbol{x}-\boldsymbol{x}_0\|^{-1})=-4\pi\delta(\boldsymbol{x}-\boldsymbol{x}_0)$
100272
Why do we select the metric tensor for raising and lowering indices?
148837
Equivalent definition of metric compatibility for a connection: what does $\nabla g$ mean?
74497
Intuitive analysis of gradient, divergence, curl
95774
$\frac{\partial^2 u}{\partial t^2}-c^2\frac{\partial^2u}{\partial x^2}=0\text{ implies } \frac{\partial^2 u}{\partial z \partial y}=0$
129481
About the term $-\nabla_{[u,v]}w$ in the definition of Riemann curvature tensor
109358
Prove the Curvature Tensor is a Tensor
41385
$\nabla U=0 \implies U=\mathrm{constant}$ only if $U$ is defined on a connected set?
149822
If $\omega \in \Omega^q(M)$, and $(\omega|_{U})_p = 0$, is $\omega_p = 0$?
140024
How to obtain the gradient in polar coordinates
40293
Understanding the definition of norm of tensors on a Riemannian manifold
42392
Derivation of Maxwell's equations from field tensor lagrangian
38613
Intuitive understanding of the elements in the stress-energy tensor