Geodesic
On real Kähler Euclidean submanifolds with non-negative Ricci curvature
Journal of the European Mathematical Society, Tome 7 (2005) no. 1, pp. 1-11

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We show that any real Kähler Euclidean submanifold f:M2n→R2n+p 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 M2n is complete. In particular, we conclude that the only real Kähler submanifolds M2n in R3n that have either positive Ricci curvature or positive holomorphic sectional curvature are precisely products of n orientable surfaces in R3 with positive Gaussian curvature. Further applications of our main result are also given.
DOI : 10.4171/jems/19
Classification : 53-XX, 00-XX
Keywords: Kähler submanifolds, Ricci curvature, holomorphic curvature 
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Luis A. Florit; Wing San Hui; Fangyang Zheng. On real Kähler Euclidean submanifolds with non-negative Ricci curvature. Journal of the European Mathematical Society, Tome 7 (2005) no. 1, pp. 1-11. doi: 10.4171/jems/19

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