<ruby id="d9npn"></ruby>

      <sub id="d9npn"><progress id="d9npn"></progress></sub>

      <nobr id="d9npn"></nobr>

      <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

      <th id="d9npn"><meter id="d9npn"></meter></th>

      Stack Exchange Network

      Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

      Visit Stack Exchange

      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].

      1
      vote
      0answers
      30 views

      Extension of Vector Field in the $\mathcal{C}^r$ topology

      This question was previously posted on MSE. Let $M\subset \mathbb{R}^n$ be a compact smooth manifold embedded in $\mathbb{R}^n$, we define $$\mathfrak{X}(M) := \{X: M \to \mathbb{R}^n;\ X\mbox{ is ...
      1
      vote
      0answers
      45 views

      Matrix trace minimization of quadratic and linear terms under orthogonal manifold constraints

      How would one solve the following orthogonal manifold problem? $$\begin{array}{ll} \text{maximize} & \mbox{tr}(X^\top A X - X^\top B)\\ \text{subject to} & X^\top X = I\end{array}$$ where $A ...
      6
      votes
      0answers
      166 views
      +100

      Structural Stability on Compact $2$-Manifolds with Boundary

      I'm studying the structural stability of vector fields and I'm interested in learning about this phenomenon on compact $2$-manifolds with boundary. Let $M^2$ be a compact connected 2-manifold and $\...
      9
      votes
      1answer
      286 views

      Smooth vector fields on a surface modulo diffeomorphisms

      Let $\Sigma$ be a two-dimensional connected smooth manifold without boundary. (Feel free to assume it is compact and orientable.) Let $\mathcal{X}(\Sigma)$ denote the smooth vector fields on $\Sigma$...
      2
      votes
      0answers
      238 views

      Integration over a Surface without using Partition of Unity

      Suppose we are given a compact Riemann surface $M$, an open cover $\mathscr{U}=\{U_1,U_2,\dots\}$ of $M$, charts $\{(U_1,\phi_1),(U_2,\phi_2),\dots\}$, holomorphic coordinates, $\phi_m:p\in U_m\mapsto ...
      1
      vote
      0answers
      206 views

      On the homotopy type of $\mathrm{Diff}(\mathbb{S}^3)$

      I am confused with the following argument. I know I am doing something wrong but I can't find my mistake. On one hand, one knows that if $M$ is a Lie group, then $$\mathrm{Diff}(M)\simeq M\times\...
      2
      votes
      0answers
      46 views

      Traceless sobolev forms on compact manifolds with boundary

      Let $(M,g)$ be a smooth, compact, oriented Riemannian manifold with smooth, oriented boundary $\partial M$. Further, let $\Omega^p(M)$ and $\Omega^p(\partial M)$ be the spaces of smooth differential $...
      0
      votes
      1answer
      328 views

      Metrics on derived smooth manifolds

      Derived geometry explains how to remove the transversality condition and make sense out of a nontransversal intersection. For example, if $X$ and $Y$ are embedded submanifolds of a manifold (or ...
      9
      votes
      0answers
      255 views

      History of the definition of smooth manifold with boundary

      I am trying to determine the earliest source for the definition of smooth ($C^\infty$) manifold with boundary. Milnor and Stasheff (1958) give a definition, but a scrutiny of that definition shows it ...
      3
      votes
      0answers
      73 views

      Quartic link in a 5-sphere

      In this post I would like to propose a quartic link in a 5-sphere. Let us start with the following gluing into a 5-sphere: $$S^5=(D^2_{} \times T^3_{}) \cup_{T^4} ({S^5 \smallsetminus D^2 \times T^3})...
      2
      votes
      0answers
      163 views

      Triple link in a 5-sphere — Proposal

      In this post I would like to propose a triple link in a 5-sphere. Let us start with the following gluing into a 5-sphere: $$S^5=(D^2_{} \times T^3_{}) \cup_{T^4} ({S^5 \smallsetminus D^2 \times T^3})$...
      4
      votes
      1answer
      171 views

      Are complete minimal submanifolds closed?

      Is it true that any complete minimal submanifold of some Riemannian manifold is closed as a subset? What about the case in which the ambient manifold is an euclidean space?
      2
      votes
      0answers
      85 views

      Condition on a Lie groupoid to be represented by manifold/group or an action groupoid

      Let $\mathcal{G}$ be a Lie groupoid. I am thinking of following questions. When do we know $\mathcal{G}$ is weakly/Morita equivalent to a Lie groupoid of the form $(G\rightrightarrows *)$ for some ...
      5
      votes
      1answer
      308 views

      Are framed manifolds cubulatable?

      Let's say an $n$-manifold is cubulated if it is glued out of cubes $[0,1]^n$ in a way that looks locally like the standard cubulation of $\mathbb R^n$. For instance, the face $[0,1]^{k-1} \times \{1\} ...
      4
      votes
      1answer
      93 views

      Smooth embedding of space forms in the Euclidean space

      I was wondering which $S^n/\Gamma$ can be smoothly embedded into $\mathbb R^{n+1}$, where $\Gamma \subset O(n+1)$ is a finite subgroup. To my knowledge, the case $n \le 3$ is known. It has been proved ...

      15 30 50 per page
      特码生肖图
      <ruby id="d9npn"></ruby>

          <sub id="d9npn"><progress id="d9npn"></progress></sub>

          <nobr id="d9npn"></nobr>

          <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

          <th id="d9npn"><meter id="d9npn"></meter></th>

          <ruby id="d9npn"></ruby>

              <sub id="d9npn"><progress id="d9npn"></progress></sub>

              <nobr id="d9npn"></nobr>

              <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

              <th id="d9npn"><meter id="d9npn"></meter></th>