  In partially linear models the dependence of the response y on (x^T,t) is
modeled through the relationship y=\x^T \beta+g(t)+\epsilon where \epsilon is
independent of (x^T,t). In this paper, estimators of \beta and g are
constructed when the explanatory variables t take values on a Riemannian
manifold. Our proposal combine the flexibility of these models with the complex
structure of a set of explanatory variables. We prove that the resulting
estimator of \beta is asymptotically normal under the suitable conditions.
Through a simulation study, we explored the performance of the estimators.
Finally, we applied the studied model to an example based on real dataset.
