query: Nonzero Jacobian implies diffeomorphism?
positive_passages.docid: 24828
positive_passages.text: surjective immersion $\mathbb{R}^2 \to \mathbb{R}^2$ which is not a diffeomorphism
negative_passages.docid: 98696
negative_passages.text: Is the exponential map ever not injective?
negative_passages.docid: 91337
negative_passages.text: Is every self-homeomorphism homotopic to a diffeomorphism?
negative_passages.docid: 148737
negative_passages.text: Is $|xy|$ differentiable in $(0,0)$?
negative_passages.docid: 102246
negative_passages.text: Are there nonsmooth Lie groups?
negative_passages.docid: 112187
negative_passages.text: Is there a way to see that $ \nabla_\mu g_{\nu \rho} = 0 $ without explicit computation, where $\nabla_\mu$ refers to the covariant derivative?
negative_passages.docid: 91322
negative_passages.text: A diffeomorphism whose tangent map preserves dot products is an isometry.
negative_passages.docid: 128410
negative_passages.text: Showing that the set of fixed points is a smooth manifold
negative_passages.docid: 127436
negative_passages.text: Conformal Maps onto the Unit Disc in $\mathbb{C}$
negative_passages.docid: 27746
negative_passages.text: Autohomeomorphism of the unit disk which is constant on the boundary, and which takes 0 to a prescribed point
negative_passages.docid: 111689
negative_passages.text: Surjective, but not injective endomorphism
negative_passages.docid: 63845
negative_passages.text: Diffeomorphism $f:U\to V$ then $Df:\mathbb{R^n}\to\mathbb{R^m}$ will be linear isomorphism hence $n=m$
negative_passages.docid: 116427
negative_passages.text: $(c^{\mu}\partial_{\mu}-m)\phi(x)=0$ not Lorentz-invariant?
negative_passages.docid: 31561
negative_passages.text: Is there a Smooth Real Manifold which is not a Riemannian Manifold?
negative_passages.docid: 137451
negative_passages.text: Does there exist a differentiable conservative vector field with non - vanishing curl?
negative_passages.docid: 132311
negative_passages.text: T$\mathbb{S}^{n} \times \mathbb{R}$ is diffeomorphic to $\mathbb{S}^{n}\times \mathbb{R}^{n+1}$
negative_passages.docid: 116750
negative_passages.text: On surjectivity of exponential map for Lie groups