  We consider models of bosons on curved 3+1 dimensional space-time embedded in
a higher dimensional flat ambient space. We propose to derive (rather than
postulate) equations of motions by assuming that a standard Klein-Gordon field
on ambient space is restricted to space-time by a strong confining potential.
This leads to a modified Klein-Gordon equation on space-time which includes, in
addition to the standard terms, a term with a so-called induced potential which
depends on intrinsic- and extrinsic curvature of the embedded space-time but
not on the details of the confining potential. We compute this induced
potential for natural, simple embeddings of Schwarzschild- and Robertson-Walker
space-times. We also discuss possible observable implications of our results
and, in particular, propose and study an extension of a standard model of
cosmological inflation taking into account extrinsic curvature effects. We show
that the modified model allows for a solution where the scaling function
vanishes like a power law with exponent 0.6830.. at some initial time.
