Rigidity of real Kaehler submanifolds
This paper deals with isometric immersions f of 2n-dimensional Kaehler manifolds into real Euclidean \((2n+p)\)-space. If the type number is at least 3, then f is holomorphic. If f is minimal, then it is circular (i.e. \(\alpha (JX,Y)=\alpha (X,JY))\), and thus the results of the first author and \textit{D. Gromoll} [J. Differ. Geom. 22, 13-28 (1985; Zbl 0587.53051)] apply. If f is minimal, then it is congruent to a holomorphic isometric immersion into \({\mathbb{C}}^{n+1}\), if such exist. For type number 3 a similar result holds in \({\mathbb{C}}^{n+q}\). The core of the proofs is a lemma on the determination of the second fundamental form by the Gauss equation generalizing a well-known result of Chern.
scientific article; zbMATH DE number 3967325