Geodesic
Isometric Immersions of almost Hermitian Manifolds
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 456-459

Voir la notice de l'article provenant de la source Cambridge University Press

The Lefschetz theorem on hyperplane sections, as proved by Andreotti and Frankel (1), depends upon the following result.THEOREM. If M is a non-singular affine algebraic variety of real dimension 2k of complex n-space, then This theorem, which is interesting in itself, has been strengthened by Milnor (7), who showed that M has the homotopy type of a k-dimensional CW-complex.In this paper we generalize the above theorem in two directions. First, we replace complex n-space by some other complete simply connected Riemannian manifold which either has non-positive curvature or is a compact symmetric space. Secondly, we allow M and to be quasi-Kâhlerian (see below) instead of Kählerian.We first introduce some notation. Let M and be C ∞ Riemannian manifolds with M isometrically immersed in . Denote by 〈, 〉 the metric tensor of either M or . 
Gray, Alfred. Isometric Immersions of almost Hermitian Manifolds. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 456-459. doi: 10.4153/CJM-1969-049-5
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