Search Results

No (independent of the full meaning of the question) in general it does not. Any manifold which admits a Lagrangian fibration to a half dimensional base, also admits a Lagrangian foliation, and hence …

The counter example given in the comments by Brian Conrad (and Dylan Thurston) is very nice. However, it oscillates wildly at $\infty$, and I believe that if you assume some nice properties at $\infty …

It is not enough to be within the injective radius. Let $(M,g)$ be an $(n+1)$-dimensional manifold and $\gamma\colon (-a,a) \to M$ a geodesic. One way to define Fermi coordinates $\phi \colon (-a,a)\ …

The answer to the first is NO. As mentioned by another answer you can use Do Carmo to prove a local result of the type: at points where the normal curvature is non-zero the 0-directions defines a fol …

I am currently working with loop spaces of manifold and finite dimensional manifolds approximating these and the following comes up very naturally: In the following piece-wise smooth means smooth on …

It seems to me that if I understood the comments to my comment correctly that the map $$\mathrm{Sp}(1) \times \mathrm{Sp}(n) \to \mathrm{SO}(4n)$$ induced by right unit quarternionic multiplaction o …

Let $G=\mathbb{Z}/2\mathbb{Z}$. Let $f\colon L \to N$ be a smooth map of connected smooth closed $n$-dimensional manifolds such that the induced map $$f^* \colon H^*(N,G) \to H^*(L,G)$$ is an isomor …

Let $B$ be a closed manifold. Let $\pi : M\to B$ be a submersion such that each fiber is a manifold without boundary. Let $f : M \to \mathbb{R}$ be a function such that the restrictions $f_x$ to each …