  An hermitian Higgs bundle is a triple $({\mathfrak E},h) = (E,\Phi, h)$,
where ${\mathfrak E}=(E,\Phi)$ is a Higgs bundle \cite{Simpson} and $(E,h)$ is
a holomorphic hermitian vector bundle \cite{Kobayashi}. As it is well known,
several results on holomorphic vector bundles can be extended to the Higgs
bundles setting. In this article we show that some classical propositions,
involving orthogonal decompositions of holomorphic hermitian vector bundles and
the second fundamental form of its holomorphic subbundles, can be extended to
hermitian Higgs bundles. The extended results concerning orthogonal
decompositions have immediate applications in Higgs bundles, and we include
them in the form of two corollaries. The extended results concerning the second
fundamental form are previously known in literature \cite{Bruzzo-Granha}. Here
we revisit these results and include alternative proofs without using local
computations.
