  A curious correspondence has been known between Landau models and non-linear
sigma models: Reinterpreting the base-manifolds of Landau models as
field-manifolds, the Landau models are transformed to non-linear sigma models
with same global and local symmetries. With the idea of the dimensional
hierarchy of higher dimensional Landau models, we exploit this correspondence
to present a systematic procedure for construction of non-linear sigma models
in higher dimensions. We explicitly derive $O(2k+1)$ non-linear sigma models in
$2k$ dimension based on the parent tensor gauge theories that originate from
non-Abelian monopoles. The obtained non-linear sigma models turn out to be
Skyrme-type non-linear sigma models with $O(2k)$ local symmetry. Through a
dimensional reduction of Chern-Simons tensor field theories, we also derive
Skyrme-type $O(2k)$ non-linear sigma models in $2k-1$ dimension, which realize
the original and other Skyrme models as their special cases. As a unified
description, we explore Skyrme-type $O(d+1)$ non-linear sigma models and
clarify their basic properties, such as stability of soliton configurations,
scale invariant solutions, and field configurations with higher winding number.
