Questions tagged [submersions]

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Density of sections of vector bundles

Let $X$ be a complex manifold, $f:V \to X$ be a (real) vector bundle and $g:V \to \mathbb{R}^n$ a submersion for some $n>0$ (here $n$ is not the same as the dimension of the fiber of the vector ...
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1answer
104 views

Do submersions induce open maps between spaces of differentiable maps?

Let $X$, $Y$ and $Z$ be smooth manifolds. Any differentiable map $f \colon Y \rightarrow Z$ induces a continuous map $f_{\ast} \colon C^{\infty}(X, Y) \rightarrow C^{\infty}(X, Z)$ via composition $g \...
2
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1answer
135 views

Pushing forward a complex structure by submersion

I have a surjective smooth map with surjective differential between two balls $\phi:B^{2n}\rightarrow B^{2k}$. Fix an integrable almost complex structure $J$ on $B^{2n}$. Assume that $\mathrm{Ker}\:d\...
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1answer
68 views

Conditions for a pushforward of a involutive vector bundle to be involutive

I know that the following statement is true, but I would like to find a reference for it so I don't have to write the proof. Do you guys have a reference? Let $\Omega$ and $\Omega'$ be smooth ...
3
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0answers
95 views

How restrictive is $[\mathcal H,\mathcal V] =0$, or weaker, $[X,A_XY] = 0$?

Let $\pi :P \to M$ be a Riemannian submersion. Let us denote by $\mathcal H$ the horizontal space of $\pi$ and by $\mathcal V$ its vertical space. I want to know restrictions and consequences of the ...
3
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0answers
196 views

A question about a paper of Bismut and Lebeau

Let $X$ be a Riemannian manifold, and $Y\hookrightarrow X$ be a closed submanifold of $X$ with normal bundle $N$ with the induced metric. Then near $Y$, we have $$dv_X(y,Z)=k(y,Z)dv_Y(y)dv_{N_y}(Z),$$...
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2answers
328 views

Riemannian submersions from complex hyperbolic space into the hyperbolic space

Is there a (canonical) Riemannian submersion from the complex hyperbolic space $\mathbb C\mathbb H^n$ into the hyperbolic space $\mathbb H^n$? In the affirmative case, what can we say about the ...
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0answers
96 views

Smooth submersions - smallest universal subclass of regular epimorphisms?

The smooth category has many problems. One is that pullbacks of regular epimorphisms need not exist. However, pullbacks along submersions always exist. It also seems that submersions are universal (i....
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0answers
263 views

If the fibers of a submersion are connected, does it mean that any 2 sections are homotopic (locally on the base)?

Is the following fact known? If yes - what is the reference? Let $\phi:X\to Y$ be a submersion of smooth manifolds with connected fibers. Let $s_0,s_1:Y\to X$ be its (smooth) sections. Then, for any $...
3
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1answer
110 views

Reference request for a result regarding density of induced probability measure under a submersion

Let $\pi: M \to N$ be a smooth submersion from a bounded open subset of $\mathbb{R}^m$ onto $ N \subset \mathbb{R}^n$, $m \geq n$. Further, let $M$ be given a probability measure $\mu$. Then the map ...
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1answer
294 views

In what sense is a generically submersive morphism of varieties subermersive over singular points?

Background/Motivation I'm currently interested in the duality theorem for projective varieties and more specifically in properties of the conormal variety over the dual variety. Let $V$ be a $k$-...
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1answer
692 views

What are the smooth manifolds in the topos of sheaves on a smooth manifold?

The category of internal locales in the Grothendieck topos of sheaves on a locale X is equivalent to the slice category over X. In other words, internal locales over X are precisely morphisms of ...
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5answers
1k views

Examples of Riemannian Submersions

Is there any example of a Riemannian submersion, which is no fibration? As far as I know, a (any) submersion is locally, but not globally, given by a fibration. The converse holds globally. ...