Why is the Ricci scalar the only independent scalar constructed from products of the metric and its first and second derivatives?
38950
On the uniqueness of the Riemann-Christoffel tensor
40023
Asymptotic behaviour of the riemannian metric in polar coordinates
140692
Existence of a complete metric on $(0,1)$
11773
Levi-Civita connection between conformal metrics
118064
Homogeneous riemannian manifolds are complete. Trouble understanding proof.
105293
Proof of the second symmetric derivative
71316
Two inner products being equal up to a scalar
9457
Compact Lie group bi-invariant metric
116427
$(c^{\mu}\partial_{\mu}-m)\phi(x)=0$ not Lorentz-invariant?
37840
Does the Levi-Civita connection determine the metric?
154488
What exactly is the difference between a Ricci-flat manifold and Minkowski space?
99154
Why is the covariant derivative of the metric tensor zero?
60981
Understanding relation between Quotient Space and $S^1$
16892
Reference request: product Borel $\sigma$-algebra of non-separable metric spaces
115295
Why are the two dot product definitions equal?
153686
Is time a Scalar or a Vector?
107290
proof of product rule of derivatives using first principle?