Weakly Lagrangian embedding and product manifolds
Bull. Korean Math. Soc. 1998 Vol. 35, No. 4, 809-815
Yanghyun Byun and Seunghun Yi
Hanyang University, Youngdong University
Abstract : We investigate when the product of two smooth manifolds admits a weakly Lagrangian embedding. We prove that, if $M^m$ and $N^n$ are smooth manifolds such that $M$ admits a weakly Lagrangian embedding into $\Bbb C^m$ whose normal bundle has a nowhere vanishing section and $N$ admits a weakly Lagrangian immersion into $\Bbb C ^n$, then $M \times N$ admits a weakly Lagrangian embedding into $\Bbb C^{m+n}$. As a corollary, we obtain that $S^m \times S^n$ admits a weakly Lagrangian embedding into $\Bbb C ^{m+n}$ if $n = 1, \,\, 3$. We investigate the problem of whether $S^m \times S^n$ in general admits a weakly Lagrangian embedding into $\Bbb C ^{m+n}$.
Keywords : weakly Lagrangian embedding, product manifold, regular homotopy
MSC numbers : 53C40
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