Conformal Kaehler Euclidean submanifolds

Abstract

Let $f:M^{2n}\to {\mathbb{R}}^{2n+\ell }$, $n\ge 5$, denote a conformal immersion into Euclidean space with codimension $\ell$ of a Kaehler manifold of complex dimension $n$ and free of flat points. For codimensions $\ell =1,2$ we show that such a submanifold can always be locally obtained in a rather simple way, namely, from an isometric immersion of the Kaehler manifold $M^{2n}$ into either ${\mathbb{R}}^{2n+1}$ or ${\mathbb{R}}^{2n+2}$, the latter being a class of submanifolds already extensively studied.

13 Pages

References in corpus (1)

• Holomorphicity of real Kaehler submanifolds

Cited by in corpus (1)

• Holomorphicity of real Kaehler submanifolds