3
votes
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172 views

What is known about analogous results of Kazdan and Warner in higher dimensions?

First let me state a Theorem due to Kazdan and Warner: ``Let M be a compact two dimensional orientable manifold. Let $f: M \rightarrow \mathbb{R}$ be a function that has the same sign as ...
5
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2answers
309 views

Is there a natural form representing the Thom class of a vector bundle, which when pulled back via the zero section represents the Euler class on the level of forms?

Let $V \rightarrow M$ be an oriented vector bundle over a compact oriented manifold $M$ equipped with a metric $h$ (the metric $h$ is a metric on the Vector bundle $V$, not on the manifold $M$). Is ...