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I have posted this question on MSE one year ago, but till now I did not received an answer. Therefore I have decided to post it here. I have difficulty in understanding the meaning of "A ...

Let $(M^{2n},\omega)$ be a symplectic manifold of dimension $2n$. Let $L^k_{\omega}:\Omega^q(M)\to \Omega^{q+2k}(M)$ be the map given by $L^k_{\omega}(\alpha)=\alpha\wedge\omega^k$. Then is it true ...

I am presently reading this paper on covariant phase space and I have difficulty understanding the following formalism developed: In the paper (section $2.2$, pg. $12$), the authors have introduced ...

A $2$- form $\alpha$ on a n- manifold $M$ is called anti symplectic if for every $x\in M$, $\{ v\in T_{x} M \mid i_{v} \alpha=0 \}$ is a $n-2$ dimensional subspace of $T_{x}M$. So we obtain a $n-2$ ...

I have already asked this question on math.stackexchange.com https://math.stackexchange.com/questions/1789476/is-there-a-matrix-that-converts-the-gradient-of-any-function-to-gradient-of-othe Now I ...

Let $X$ be a compact smooth manifold that admits symplectic and Kaehler structures. There is a paper by Ugarte, Rudyak, Tralle, and Ibanez, showing how the Lefschetz rank can vary along a path of ...