  In this paper we study some variants of Dirac-type problems in hypergraphs.
First, we show that for $k\ge 3$, if $H$ is a $k$-graph on $n\in k\mathbb N$
vertices with independence number at most $n/p$ and minimum codegree at least
$(1/p+o(1))n$, where $p$ is the smallest prime factor of $k$, then $H$ contains
a perfect matching. Second, we show that if $H$ is a $3$-graph on $n\in
3\mathbb N$ vertices which does not contain any induced copy of $K_4^-$ (the
unique $3$-graph with $4$ vertices and $3$ edges) and has minimum codegree at
least $(1/3+o(1)))n$, then $H$ contains a perfect matching. Moreover, if we
allow the matching to miss at most $3$ vertices, then the minimum degree
condition can be reduced to $(1/6+o(1)))n$. Third, we show that if $H$ is a
$3$-graph on $n\in 4\mathbb N$ vertices which does not contain any induced copy
of $K_4^-$ and has minimum codegree at least $(1/8+o(1)))n$, then $H$ contains
a perfect $Y$-tiling, where $Y$ represents the unique $3$-graph with $4$
vertices and $2$ edges. We also provide the examples showing that our minimum
codegree conditions are asymptotically best possible. Our main tool for finding
the perfect matching is a characterization theorem that characterizes the
$k$-graphs with minimum codegree at least $n/k$ which contain a perfect
matching.
