  We introduce two new curvatures which refine and elucidate the real
bisectional curvature considered by Yang-Zheng \cite{YangZheng}. A unified
perspective of the various forms of the Schwarz lemma is given, leading to
novel Chern-Lu, Aubin-Yau, and Chen-Cheng-Look Schwarz lemmas in both the
K\"ahler and Hermitian category.
