Integral manifolds of contact distributions

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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 , in an arbitrary totally real -dimensional direction is established. A Legendre submanifold with these initial data is not unique in general, but in the case of a -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 -contact manifold is a Sasakian space form. Each Blair submanifold of a Sasakian space form of -holomorphic sectional curvature is a space of constant curvature . Applications of these results to the geometry of principal toroidal bundles are found.