  Jacobi theta functions with rational characteristics can be viewed as
vector-valued Jacobi forms. Theta relations usually correspond to different
constructions of certain Jacobi forms. From this observation, we extract a new
approach, which is called orbits of Jacobi forms, to produce identities on
Jacobi theta functions. Our approach not only provides simple proofs of many
known theta relations but also produces a large number of new identities, which
can be considered as generalizations of Riemann's theta relations.
