<em id="zlul0"></em>

<dl id="zlul0"></dl>
<div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
<em id="zlul0"></em>

<div id="zlul0"><ol id="zlul0"></ol></div>

# Questions tagged [smooth-manifolds]

Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].

771 questions
35 views

### Geonetry Manifold

Suppose $M$ and $N$ are $C^r$ manifolds, $r > 1$. Show that $T(M \times N)$ is $C^r>1$ diffeomorphic to $TM \times TN$.
96 views

### Asymptotic bound on minimum epsilon cover of arbitrary manifolds

Let $M \subset \mathbb{R}^d$ be a compact smooth $k$-dimensional manifold embedded in $\mathbb{R}^d$. Let $\mathcal{N}(\varepsilon)$ denote the minimal cardinal of an $\varepsilon$-cover $P$ of $M$; ...
67 views

### Subdividing a Compact Bounded Curvature Manifold into Charts with Bounded Lipschitz Constant

Let $M \subset \mathbb{R}^d$ be a compact smooth $k$-dimensional manifold embedded in $\mathbb{R}^d$. Let $\mathcal{N}(\epsilon)$ denote the size of the minimum $\epsilon$ cover $P$ of $M$; that is ...
137 views

This question was previously posted on MSE. Let $M, N$ be smooth connected manifolds (without boundary), where $M$ is a compact manifold, so we can put a topology in the space $\mathcal C^\infty(M, N)... 1answer 102 views ### Symmetric and anti-symmetric parts of the covariant derivative of a connection The following is an excerpt from Sharpe's Differential Geometry - Cartan's Generalization of Klein's Erlangen Program. Now we come to the question of higher derivatives. As usual in modern ... 0answers 158 views ### Why do unstable manifolds of two close point intersect each other in Baker map? Let$M$be$S^1 \times [-1,1]$,$f$a baker map on$M$and for$p, q \in M$consider$W^s_p$the stable manifold in$p$(i.e. the set of points whose forward orbit tend to the forward orbit of$p$) ... 0answers 92 views ### Euler-Lagrange equations on a differentiable manifold I am following the conventions of https://arxiv.org/abs/math-ph/9902027 Let$M$be a differentiable manifold,$E \to M$a vector bundle over$M$with fibre$F$,$J^1(E)$the rank-one jet bundle over$...
278 views

### Does every large $\mathbb{R}^4$ embed in $\mathbb{R}^5$?

This question was prompted by my answer to this question. An exotic $\mathbb{R}^4$ is a smooth manifold homeomorphic to $\mathbb{R}^4$ which is not diffeomorphic to $\mathbb{R}^4$ with its standard ...
147 views

### Local diffeomorphism on a neighborhood of an embedding

In my reading of the (excellent!) paper of Grabowski and Rotkiewicz on higher vector bundles (https://arxiv.org/abs/math/0702772), I have encountered the following argument which I do not understand. ...
247 views

Let $G(r,n-r)$ be the Grassmannian, which can be identified with the space of all rank $r$ projection matrices in $\mathbb{R}^n$. Let $\mu$ be the uniform measure on $G(r,n-r)$. For any $\lambda_1,...... 0answers 61 views ### Uniqueness of Fano varieties It is a theorem of Kollár–Miyaoka–Mori that there is a finite number of deformation families of smooth, complex Fano$n$-folds for each$n$(hence also a finite number of diffeomorphism types). My ... 1answer 122 views ### Are normal coordinates the same as Cartesian coordinates in flat space? Let$\gamma_v$be the unique maximal geodesic with initial conditions$\gamma_v(0)=p$and$\gamma_v'(0)=v$then the exponential map is defined by $$\exp_p(v)=\gamma_v(1)$$ If we pick any orthonormal ... 1answer 382 views ### Wu formula for manifolds with boundary The classical Wu formula claims that if$M$is a smooth closed$n$-manifold with fundamental class$z\in H_n(M;\mathbb{Z}_2)$, then the total Stiefel-Whitney class$w(M)$is equal to$Sq(v)$, where$v=...
149 views

### Extending Green's theorem from very special regions to more general regions

Green's theorem Let $C$ be a positively oriented and consists of a finite union of disjoint,piecewise smooth simple closed curve in a plane, and let $D$ be the region bounded by $C$. If $P$ and $Q$ ...
81 views

### Same fiber of induced covering map [closed]

Consider a holomorphic map $h: X \to E$ between compact, connected, complex analytic manifolds Let $p: \tilde{E}\to E$ be the universal cover, and denote by $\tilde{h}: \tilde{X}\to\tilde{E}$ the pull-...

15 30 50 per page
山西福彩快乐十分钟

<em id="zlul0"></em>

<dl id="zlul0"></dl>
<div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
<em id="zlul0"></em>

<div id="zlul0"><ol id="zlul0"></ol></div>