  In this paper, we prove an intersection-theoretic result pertaining to curves
in certain Hilbert modular surfaces in positive characteristic. Specifically,
we show that given two appropriate curves C,D parameterizing abelian surfaces
with real multiplication, the set of points (x,y) in the product CxD with
surfaces parameterized by x and y isogenous to each other is Zariski dense in C
x D, thereby proving a case of a just-likely intersection conjecture. We also
compute the change in Faltings height under appropriate p-power isogenies of
abelian surfaces with real multiplication over characteristic p global fields.
