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Immersion of Kähler manifolds in the class of convex submanifolds

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Abstract

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.

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  1. Sumy State University, Sumy, Ukraine

    A. A. Borisenko

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  1. A. A. Borisenko
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Correspondence to A. A. Borisenko.

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Original Russian Text © A. A. Borisenko, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 4, pp. 504–509.

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Borisenko, A.A. Immersion of Kähler manifolds in the class of convex submanifolds. Math Notes 100, 526–530 (2016). https://doi.org/10.1134/S0001434616090236

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  • DOI: https://doi.org/10.1134/S0001434616090236

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