Geodesic
Immersion of K\"ahler Manifolds in the Class of Convex Submanifolds
Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 504-509

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that a real complete convex Kähler submanifold in Euclidean space splits as a metric product of two-dimensional surfaces of positive Gaussian curvature in Euclidean 3-space and a Euclidean subspace. A theorem of V. K. Beloshapka and S. N. Bychkov is generalized to the case of convex submanifolds of any codimension.
Keywords: Kähler manifold, convex submanifold, extrinsic null-index, pluriharmonicity index. 
@article{MZM_2016_100_4_a2,
     author = {A. A. Borisenko},
     title = {Immersion of {K\"ahler} {Manifolds} in the {Class} of {Convex} {Submanifolds}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {504--509},
     publisher = {mathdoc},
     volume = {100},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a2/}
}
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A. A. Borisenko. Immersion of K\"ahler Manifolds in the Class of Convex Submanifolds. Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 504-509. http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a2/