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affine connection affine normal affine transformation assume compact complex contact structure complex manifold complex number complex structure components condition connexion consider constant contact manifold contact structure contradiction converges coordinate neighborhood Corollary covariantly defined denote dimension entire function equivalent exists finite geodesic submanifold Hence holomorphic hyperdistribution hypersurface imaginary axis immersion implies induced infinitesimal affine transformation infinitesimal isometries infinitesimal variation inner subgroup integer invariant submanifold Ishihara isometric Kahlerian manifold KODAI MATH Lemma Let f(z Lie algebra linear mapping meromorphic necessary and sufficient non-zero normal bundle normal variation obtain open subset orthogonal parallel planar geodesic polynomial pre-Radon measure projective space proof of Theorem Proposition prove pseudo-conformal Radon measure real axis real hypersurface real number respect Riemannian manifold Riemannian space Sasakian manifold satisfies sequence subgroup of G tangent tensor field Theorem 3.1 topological space torsionless totally geodesic unit vector vector field vectoriel Yano zeros