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We advance previous studies on decomposed Richelot isogenies(Katsura--Takashima (ANTS 2020) and Katsura (ArXiv 2021)) which are useful foranalysing superspecial Richelot isogeny graphs in cryptography. We first give acharacterization of decomposed Richelot isogenies between Jacobian varieties ofhyperelliptic curves of any genus. We then define generalized Howe curves, andpresent two theorems on their relationships with decomposed Richelot isogenies.We also give new examples including a non-hyperelliptic (resp.\,hyperelliptic)generalized Howe curve of genus 5 (resp.\,of genus 4).

Decomposed Richelot isogenies of Jacobian varieties of hyperelliptic curves and generalized Howe curves