We compute the curvature tensor of the tangent bundle of a Riemannian manifold endowed with a natural metric and we get some relationships between the geometry of the base manifold and the geometry of the tangent bundle.

Under a partly linear model we study a family of robust estimates for the regression parameter and the regression function when some of the predictors take values on a Riemannian manifold. We obtain the consistency and the ...

In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link (proved in Giambo ...

It is established that every self-contracted curve in a Riemannian manifold has finite length, provided its image is contained in a compact set.

We use the Hessian - Weitzenböck formula to simplify the exposition of several well known theorems. We present a uni ed treatment of the theorems of Lichnerowicz - Obata, Reilly and Escobar regarding the rst eigenvalue ...

In this paper, we consider kernel type estimator with variable bandwidth when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. ...

We consider the problem of finding a singularity of a differentiable vector field X defined on a complete Riemannian manifold. We prove a unified result for theexistence and local uniqueness of the solution, and for the ...

In partly linear models, the dependence of the response y on (xT, t) is modeled through the relationship y = xTβ + g(t) + ε, where ε is independent of (xT, t). We are interested in developing an estimation procedure that ...