  Let $G$ be a connected non-odd-bipartite hypergraph with even uniformity. The
least H-eigenvalue of the signless Laplacian tensor of $G$ is simply called the
least eigenvalue of $G$ and the corresponding H-eigenvectors are called the
first eigenvectors of $G$. In this paper we give some numerical and structural
properties about the first eigenvectors of $G$ which contains an odd-bipartite
branch, and investigate how the least eigenvalue of $G$ changes when an
odd-bipartite branch attached at one vertex is relocated to another vertex. We
characterize the hypergraph(s) whose least eigenvalue attains the minimum among
a certain class of hypergraphs which contain a fixed non-odd-bipartite
connected hypergraph. Finally we present some upper bounds of the least
eigenvalue and prove that zero is the least limit point of the least
eigenvalues of connected non-odd-bipartite hypergraphs.
