论文标题
真正的Kaehler Submanifolds最多四个
Real Kaehler submanifolds in codimension up to four
论文作者
论文摘要
令$ f \ colon m^{2n} \ to \ mathbb {r}^{2n+4} $是复杂尺寸$ n \ geq 5 $ in Euclidean Space的kaehler歧管的等距沉浸，至少无处不在$ 5 $。 Our main result is that, along each connected component of an open dense subset of $M^{2n}$, either $f$ is holomorphic in $\mathbb{R}^{2n+4}\cong\mathbb{C}^{n+2}$ or it is in a unique way a composition $f=F\circ h$ of isometric immersions.在后一种情况下，我们有$ h \ colon m^{2n} \ to n^{2n+2} $是全态，$ f \ colon n^{2n+2} \ to \ mathbb {r}^{r}^{2n+4} $属于该类，属于该类别，属于Non nor nor non nor nor non nor non non non nor ke。此外，当$ f $很少时，Submanifold $ f $很少。
Let $f\colon M^{2n}\to\mathbb{R}^{2n+4}$ be an isometric immersion of a Kaehler manifold of complex dimension $n\geq 5$ into Euclidean space with complex rank at least $5$ everywhere. Our main result is that, along each connected component of an open dense subset of $M^{2n}$, either $f$ is holomorphic in $\mathbb{R}^{2n+4}\cong\mathbb{C}^{n+2}$ or it is in a unique way a composition $f=F\circ h$ of isometric immersions. In the latter case, we have that $h\colon M^{2n}\to N^{2n+2}$ is holomorphic and $F\colon N^{2n+2}\to\mathbb{R}^{2n+4}$ belongs to the class, by now quite well understood, of non-holomorphic Kaehler submanifold in codimension two. Moreover, the submanifold $F$ is minimal if and only if $f$ is minimal.
