query: Why are Compact Steady and Expanding Solitons always Einstein Manifolds?
positive_passages.docid: 19409
positive_passages.text: How to prove the expanding Ricci soliton is Einstein metric?
negative_passages.docid: 150407
negative_passages.text: Gravitational wave solutions to the Einstein field equations
negative_passages.docid: 110691
negative_passages.text: Proving that given any two points in a connected manifold, there exists a diffeomorphism taking one to the other
negative_passages.docid: 40338
negative_passages.text: Ordinary Differential Equations used in Cosmology
negative_passages.docid: 153929
negative_passages.text: White Hole Formation and Queries
negative_passages.docid: 61603
negative_passages.text: Why is the Yang–Mills existence and mass gap problem so fundamental?
negative_passages.docid: 68906
negative_passages.text: Do the same equations of motion imply the same Lagrangians?
negative_passages.docid: 71085
negative_passages.text: In Einstein's General Relativity, do the space-time dimensions curve?
negative_passages.docid: 12272
negative_passages.text: Why $a$ is not an essential singularity and how $f$ can be extended
negative_passages.docid: 116427
negative_passages.text: $(c^{\mu}\partial_{\mu}-m)\phi(x)=0$ not Lorentz-invariant?
negative_passages.docid: 115142
negative_passages.text: Holomorphic functions on a complex compact manifold are only constants
negative_passages.docid: 142605
negative_passages.text: Do particles in a black hole stay in constant orbit?
negative_passages.docid: 101090
negative_passages.text: Why exactly do sometimes universal covers, and sometimes central extensions feature in the application of a symmetry group to quantum physics?
negative_passages.docid: 55534
negative_passages.text: Why one-dimensional strings, but not higher-dimensional shells/membranes?
negative_passages.docid: 67641
negative_passages.text: Why should field operators satisfy the classical equations of motion?
negative_passages.docid: 154488
negative_passages.text: What exactly is the difference between a Ricci-flat manifold and Minkowski space?
negative_passages.docid: 38127
negative_passages.text: Equivalence between Kähler condition and $\partial_kg_{i\bar j} = \partial_ ig_{k\bar j}$