query: (Scalar) Ricci flatness of a metric
positive_passages.docid: 5247
positive_passages.text: Physical meaning of non-trivial solutions of vacuum Einstein's field equations
negative_passages.docid: 67357
negative_passages.text: Geodesics equations via variational principle
negative_passages.docid: 151285
negative_passages.text: Existence of a local geodesic frame
negative_passages.docid: 127034
negative_passages.text: Let $\rho(x,y)= \frac{d(x,y)}{1+d(x,y)}$, show that $\rho$ is a metric equivalent to $d$
negative_passages.docid: 74607
negative_passages.text: Variation of the metric with respect to the metric
negative_passages.docid: 118064
negative_passages.text: Homogeneous riemannian manifolds are complete. Trouble understanding proof.
negative_passages.docid: 127631
negative_passages.text: On a conformal mapping
negative_passages.docid: 59833
negative_passages.text: Isometric embedding of Schwarzchild metric in $\mathbb{R}^4$
negative_passages.docid: 9457
negative_passages.text: Compact Lie group bi-invariant metric
negative_passages.docid: 99154
negative_passages.text: Why is the covariant derivative of the metric tensor zero?
negative_passages.docid: 129481
negative_passages.text: About the term $-\nabla_{[u,v]}w$ in the definition of Riemann curvature tensor
negative_passages.docid: 90365
negative_passages.text: Riemannian Manifolds with $n(n+1)/2$ dimensional symmetry group
negative_passages.docid: 121914
negative_passages.text: Unitary representations of the diffeomorphism group in curved spacetime
negative_passages.docid: 152476
negative_passages.text: Unique Perpendicular Geodesic
negative_passages.docid: 14652
negative_passages.text: Proof a $(2n-1)$-compact manifold
negative_passages.docid: 123061
negative_passages.text: $X$ metric separable then $C(X)$ separable
negative_passages.docid: 122352
negative_passages.text: Topologies in a Riemannian Manifold