Hom-Lie superalgebra structures on infinite-dimensional simple Lie superalgebras of vector fields

This paper considers eight series of infinite-dimensional simple Lie superalgebras of vector fields over a field of characteristic zero. It is proved that Hom-Lie superalgebra structures on these Lie superalgebras must be scalars. As a consequence, multiplicative Hom-Lie superalgebra structures on these Lie superalgebras must be zero or the identity automorphisms.