# User contributions

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- 17:05, 10 May 2021
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**+766** N Definition:Horizontal Vector Field Created page with "== Definition == Let $M$ be a smooth manifold. Let $x \in M$ be a base point. Let $H_x$ be the Definition:Horizon..." current - 16:44, 10 May 2021
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**+893** N Definition:Horizontal Tangent Space Created page with "== Definition == Let $M, \tilde M$ be smooth manifolds. Let $\tilde g$ be a Riemannian metric on $\tilde M$...." current - 16:42, 10 May 2021 diff hist +13 m Definition:Vertical Tangent Space current
- 16:37, 10 May 2021
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**+857** N Definition:Vertical Tangent Space Created page with "== Definition == Let $M, \tilde M$ be smooth manifolds. Let $\tilde g$ be a Riemannian metric on $\tilde M$...." - 16:17, 10 May 2021
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**-1,169** m User:Julius current - 20:36, 9 May 2021
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**+1,126** N Definition:Product Riemannian Metric Created page with "== Definition == Let $\struct {M_1, g_1}$ and $\struct {M_2, g_2}$ be Riemannian manifolds. Let $p \in M$ be a Definition:Base Point|bas..." current - 20:02, 9 May 2021
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**+640** m User:Julius - 20:01, 9 May 2021
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**+2,633** N Mixed Partial Derivative of Heaviside Step Function Created page with "== Theorem == Let $\tuple {x, y} \stackrel u {\longrightarrow} \map u {x, y}: \R^2 \to \R$ be the Heaviside step function..." current - 19:27, 9 May 2021 diff hist +155 m Definition:Dirac Delta Distribution current
- 21:42, 6 May 2021
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**+903** N Definition:Smooth Local Parametrization Created page with "== Definition == Let $\tilde M$ be a smooth manifold. Let $M \subseteq \tilde M$ be a submanifold. Let $U \subsete..." current - 21:21, 6 May 2021
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**+872** N Definition:Normal Vector Field along Submanifold Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$ be a Riemannian manifold. Let $M : M \subseteq \tilde M$ be a Definition:Smooth Mani..." current - 21:00, 6 May 2021 diff hist +313 m User:Julius
- 17:05, 5 May 2021
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**+1,128** N Definition:Frame Adapted to Submanifold Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$ be an $m$-dimensional Definition:Riemannian Manifold|Riemannian mani..." current - 16:44, 5 May 2021 diff hist +498 N Definition:Riemannian Submanifold Created page with "== Definition == Let $M$ be an immersed submanifold. Let $g$ be a Definition:Induced Metric on Submanifold|metric induc..." current
- 16:41, 5 May 2021 diff hist -8 m Definition:Induced Metric on Submanifold current
- 16:39, 5 May 2021
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**+739** N Definition:Induced Metric on Submanifold Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$ be a Riemannian manifold. Let $M : M \subseteq \tilde M$ be a Definition:Smooth Mani..." - 16:16, 5 May 2021 diff hist +41 m User:Julius
- 19:22, 4 May 2021 diff hist +49 m Definition:Metric Induced by Smooth Immersion current
- 19:19, 4 May 2021
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**+537** N Definition:Isometric Immersion Created page with "== Definition == Let $\struct {M, g}$, $\struct {\tilde M, \tilde g}$ be Riemannian manifolds. Let $F : M \to \tilde M$ be an Definition..." current - 19:06, 4 May 2021
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**+565** N Definition:Metric Induced by Smooth Immersion Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$ be a Riemannian manifold. Let $F : M \to \tilde M$ be a smooth [..." - 18:52, 4 May 2021
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**+769** N Definition:Orthonormal Frame Created page with "== Definition == Let $M$ be a Riemannian manifold. Let $U \subseteq M$ be an open set. Let $p \in M$ b..." current - 18:28, 4 May 2021
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**-655** m User:Julius - 18:28, 4 May 2021
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**+1,155** N Definition:Heaviside Step Function/Two Variables Created page with "== Definition == <onlyinclude> Let $u: \R \to \R$ be the Heaviside step function. Then the '''Heaviside step function of two variables..." current - 17:57, 4 May 2021 diff hist +159 m Definition:Heaviside Step Function current
- 17:55, 4 May 2021 diff hist +1 m Distributional Partial Derivatives Commute current
- 17:54, 4 May 2021
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**+1,551** N Distributional Partial Derivatives Commute Created page with "== Theorem == Let $T \in \map {\DD'} {\R^d}$ be a distribution. Then in the distributional sense: :$\d..." - 16:19, 3 May 2021
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**+728** N Definition:Local Frame Created page with "== Definition == Let $M$ be a smooth manifold. Let $U \subseteq M$ be an open set. Let $\sigma = \tuple {\..." current - 15:52, 3 May 2021 diff hist +9 m Definition:Warped Product Manifold current
- 15:51, 3 May 2021 diff hist +498 m User:Julius
- 15:51, 3 May 2021 diff hist 0 m Definition:Warped Product Manifold Julius moved page Definition:Warped Product to Definition:Warped Product Manifold without leaving a redirect
- 15:48, 3 May 2021 diff hist +125 m Definition:Distributional Derivative current
- 15:44, 3 May 2021
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**+2,204** N Set of Distributional Derivatives of Dirac Delta Distribution is Linearly Independent Created page with "== Theorem == Let $\delta \in \map {\DD'} \R$ be the Dirac delta distribution. Then for any $n \in \N$ the set of..." current - 21:59, 2 May 2021 diff hist +189 m User:Julius
- 21:58, 2 May 2021 diff hist +27 m Definition:Zero Mapping/Distribution current
- 21:58, 2 May 2021 diff hist +105 m Definition:Zero Mapping current
- 21:57, 2 May 2021 diff hist +50 N Definition:Zero Distribution Redirected page to Definition:Zero Mapping/Distribution current Tag: New redirect
- 21:57, 2 May 2021 diff hist +359 N Definition:Zero Mapping/Distribution Created page with "== Definition == Let $\map \DD \R$ be the test function space. Let $\mathbf 0 \in \map {\DD'} \R$ be a Definition:Distribution|distribut..."
- 21:40, 29 April 2021
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**+1,475** N Definition:Warped Product Manifold Created page with "== Definition == Let $\struct {M_1, g_1}$, $\struct {M_2, g_2}$ be Riemannian manifolds. Let $f : M_1 \to \R_{\mathop > 0}$ be a Definit..." - 21:00, 29 April 2021 diff hist +287 m User:Julius
- 08:13, 29 April 2021 diff hist +45 m Fundamental Solution to 1D Laplace's Equation current
- 21:35, 28 April 2021 diff hist +126 m User:Julius
- 21:22, 28 April 2021
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**+583** N Definition:Riemannian Covering Created page with "== Definition == Let $\struct {M, g}$ and $\struct {\tilde M, \tilde g}$ be Riemannian manifolds. Let $\pi : \tilde M \to M$ be a Defini..." current - 21:11, 28 April 2021
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**-635** m Fundamental Solution to 1D Laplace's Equation - 21:03, 28 April 2021
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**+1,357** N Distributional Derivatives of Dirac Delta Distribution do not Vanish Created page with "== Theorem == Let $\delta \in \map {\DD'} \R$ be the Dirac delta distribution. Then for any $n \in \N$ the Definition:Distribution..." current - 07:34, 28 April 2021 diff hist +179 m Fundamental Solution to 1D Laplace's Equation
- 19:35, 27 April 2021
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**+1,186** N Definition:Riemannian Submersion Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$, $\struct {M, g}$ be Riemannian manifolds. Let $\pi : \tilde M \to M$ be a Definitio..." current - 18:51, 27 April 2021
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**-1,160** m User:Julius - 18:26, 27 April 2021
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**+2,291** N Fundamental Solution to 1D Laplace's Equation Created page with "== Theorem == Let $\ds \map f x = \frac {\size x} 2$ where $\size x$ is the absolute value function. Let $\delta \in \map {\DD'} \..." - 17:39, 26 April 2021
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**+1,010** N Definition:Normal Space/Manifold Created page with "== Definition == Let $\struct {\tilde M, \tilde g}$ be a Riemannian manifold. Let $M \subseteq \tilde M$ be a Definition:Smooth Manifold..." current - 16:43, 26 April 2021
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**+687** N Definition:Normal Bundle Created page with "== Definition == Let $M$ be a differentiable manifold. Let $p \in M$ be a point in $M$. Let $N_p M$ be the..." current