0
votes
0answers
43 views

Seifert manifolds

Seifert fiber space is a PFB. The theorem states that every principal fiber bundle (PFB) admits a connection form, so how can we define the connection 1-form on it? Or how can I find a book or article ...
2
votes
2answers
92 views

Manifold non-orientable iff. frame bundle is connected

Let $M$ be a connected smooth manifold and $L(M):=\bigcup_{x\in M}L_xM$ its frame bundle where $L_xM:=\{(v_1,\dots,v_n):\{v_1,\dots,v_n\}\text{ is a basis of }T_xM\}$. $M$ is non-orientable iff. ...
5
votes
1answer
112 views

One-form on quotient manifold

Let $M$ be a smooth manifold with tangent bundle $TM$ and cotangent bundle $TM^*$ and $\psi\in TM^*$ a one-form. We denote the quotient manifold of $M$ by the free and proper $G$-action $\varphi$ as ...