Let H=(V,E) be an r-uniform hypergraph on n vertices. The signless Laplacian spectral radius of H is defined as the maximum modulus of the eigenvalues of the tensor Q(H)=D(H)+A(H)
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, where
D(H)
and
A(H)
are the degree diagonal tensor and the adjacency tensor of
H
, respectively. In this paper, we establish a general theorem that extends the spectral Turán result of Keevash, Lenz and Mubayi [SIAM J. Discrete Math., 28 (4) (2014)] to the setting of signless Laplacian spectral Turán problems. We prove that if a family
F
of
r
-uniform hypergraphs is degree-stable with respect to a family
Hn
of
r
-uniform hypergraphs and its extremal constructions satisfy certain natural assumptions, then the signless Laplacian spectral Turán problem for
F
can be effectively reduced to the corresponding problem restricted to the family
Hn
. As a concrete application, we completely determine the extremal hypergraph that maximizes the signless Laplacian spectral radius among all Fano plane-free
3
-uniform hypergraphs, showing that the unique extremal hypergraph is the balanced complete bipartite
3
-uniform hypergraph.
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