JournalsjemsVol. 7, No. 1pp. 1–11

On real Kähler Euclidean submanifolds with non-negative Ricci curvature

  • Luis A. Florit

    Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
  • Wing San Hui

    Ohio State University, Columbus, USA
  • Fangyang Zheng

    Ohio State University, Columbus, USA
On real Kähler Euclidean submanifolds with non-negative Ricci curvature cover
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Abstract

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 2n2p2n-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 M2nM^{2n} is complete. In particular, we conclude that the only real K\"ahler submanifolds M2nM^{2n} in R3n\R^{3n} that have either positive Ricci curvature or positive holomorphic sectional curvature are precisely products of nn orientable surfaces in R3\R^3 with positive Gaussian curvature. Further applications of our main result are also given.

Cite this article

Luis A. Florit, Wing San Hui, Fangyang Zheng, On real Kähler Euclidean submanifolds with non-negative Ricci curvature. J. Eur. Math. Soc. 7 (2005), no. 1, pp. 1–11

DOI 10.4171/JEMS/19