  In this paper, we present strongly geodesic preinvexity on Riemannian
manifolds (RM) and strongly {\eta}-invexity of order m on RM. Furthermore, we
define strongly invariant {\eta}-monotonicity of order m on RM. Under Condition
C, an important characterization of these functions are studied. We construct
several non-trivial examples in support of these definitions. Afterwords, an
important and significant characterization of a strict {\eta}-minimizers
({\eta}-minimizers)of order m for MOP and a solution to the variational
like-inequality problem (VVLIP) has been derived.
