Geodesic
Integral manifolds of contact distributions
Sbornik. Mathematics, Tome 189 (1998) no. 12, pp. 1855-1870 Cet article a éte moissonné depuis la source Math-Net.Ru

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The existence of an integral manifold of the contact distribution (a Legendre submanifold) that passes through an arbitrary point in a contact manifold $M^{2n+1}$, in an arbitrary totally real $n$-dimensional direction is established. A Legendre submanifold with these initial data is not unique in general, but in the case of a $K$-contact manifold of dimension greater than 5 the set of these submanifolds is shown to contain a totally geodesic submanifold (which is called a Blair submanifold in the paper) if and only if this $K$-contact manifold is a Sasakian space form. Each Blair submanifold of a Sasakian space form of $\Phi$-holomorphic sectional curvature $c$ is a space of constant curvature $(c+3)/4$. Applications of these results to the geometry of principal toroidal bundles are found. 
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V. F. Kirichenko; I. P. Borisovskii. Integral manifolds of contact distributions. Sbornik. Mathematics, Tome 189 (1998) no. 12, pp. 1855-1870. http://geodesic.mathdoc.fr/item/SM_1998_189_12_a7/

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