On real Kähler Euclidean submanifolds with non-negative Ricci curvature

• Autores: Wing San Hui, Luis A. Florit, Fangyang Zheng
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 7, Nº 1, 2005, págs. 1-12
• Idioma: inglés
• DOI: 10.4171/jems/19
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• Resumen

  • We show that any real K\"ahler Euclidean submanifold \fk with either non-negative Ricci curvature or non-negative holomorphic sectional curvature has index of relative nullity greater than or equal to $2n-2p$. Moreover, if equality holds everywhere, then the submanifold must be a product of Euclidean hypersurfaces almost everywhere, and the splitting is global provided that $M^{2n}$ is complete. In particular, we conclude that the only real K\"ahler submanifolds $M^{2n}$ in $\R^{3n}$ that have either positive Ricci curvature or positive holomorphic sectional curvature are precisely products of $n$ orientable surfaces in $\R^3$ with positive Gaussian curvature. Further applications of our main result are also given.