A new version of the second main theorem for meromorphic mappings intersecting hyperplanes in several complex variables

Let c∈Cmc∈Cm, f:Cm→Pn(C)f:Cm→Pn(C) be a linearly nondegenerate meromorphic mapping over the field PcPc of c  -periodic meromorphic functions in CmCm, and let HjHj(1≤j≤q)(1≤j≤q) be q(>2N−n+1)q(>2N−n+1) hyperplanes in N  -subgeneral position of Pn(C)Pn(C). We prove a new version of the second main theorem for meromorphic mappings of hyperorder strictly less than one without truncated multiplicity by considering the Casorati determinant of f instead of its Wronskian determinant. As its applications, we obtain a defect relation, a uniqueness theorem and a difference analogue of generalized Picard theorem.