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Abstract. Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. The main purpose of this paper is to completely classify all non-minimal ideal submanifolds of real space forms with type number ≤ 2.

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It is known that applying an scriptH‐homothetic deformation to a complex contact manifold whose vertical space is annihilated by the curvature yields a condition which is invariant under scriptH‐homothetic deformations. A complex contact manifold satisfying this condition is said to be a complex (κ,μ)‐space. In this paper, we deal with the questions of Bochner, conformal and conharmonic flatness of complex (κ,μ)‐spaces when κ<1, and prove that such kind of spaces cannot be Bochner flat, conformally flat or conharmonically flat.