query: Are Riemannian Geometry and Differential topology the same thing?
positive_passages.docid: 145937
positive_passages.text: Differential topology versus differential geometry
negative_passages.docid: 143929
negative_passages.text: dimension of a connected Manifold
negative_passages.docid: 128481
negative_passages.text: Can two different topological spaces cover each other?
negative_passages.docid: 151407
negative_passages.text: Recommending books for introductory differential geometry
negative_passages.docid: 78108
negative_passages.text: Do these define metrics on $\mathbb{R}$?
negative_passages.docid: 11319
negative_passages.text: Is $M=\{(x,|x|): x \in (-1, 1)\}$ not a differentiable manifold?
negative_passages.docid: 90365
negative_passages.text: Riemannian Manifolds with $n(n+1)/2$ dimensional symmetry group
negative_passages.docid: 73172
negative_passages.text: Is every complex (smooth) manifold a scheme?
negative_passages.docid: 99755
negative_passages.text: Non-orientable 1-dimensional (non-hausdorff) manifold
negative_passages.docid: 113688
negative_passages.text: Is Topological Space a Metric Space?
negative_passages.docid: 96781
negative_passages.text: connected manifolds are path connected
negative_passages.docid: 56960
negative_passages.text: How can I show that circles in the complex plane correspond to circles on the Riemann sphere? How about lines?
negative_passages.docid: 46608
negative_passages.text: For any smooth manifold, is it true that for any two points on the manifold, there exists a chart that covers the two points?
negative_passages.docid: 258
negative_passages.text: Existence of orthogonal coordinates on a Riemannian manifold
negative_passages.docid: 60236
negative_passages.text: What is the difference between topological and metric spaces?
negative_passages.docid: 76937
negative_passages.text: Is there an elementary way to see that there is only one complex manifold structure on $R^2$?
negative_passages.docid: 42051
negative_passages.text: Book covering differential geometry and topology for physics