We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.

The analysis of manifold-valued data requires efficient tools from Riemannian geometry to cope with the computational complexity at stake. This complexity arises from the always-increasing dimension of the data, and the absence of closed-form expressions to basic operations such as the Riemannian logarithm. In this paper, we adapt a generic numerical scheme recently introduced for computing par...

We produce new examples of harmonic maps, having as either source or target manifold the tangent bundle TM on a Riemannian manifold (M,g), equipped with a Riemannian g-natural metric G. In particular, we study the harmonicity of the canonical projection π : (TM,G)→ (M,g), and of the identity map (TM,G)→ (TM,gS) and conversely, gS being the Sasaki metric on TM. A corresponding study is made for ...

The \classical case" is the case in which X is a compact riemannian manifold and D is the (positive de nite) Laplacian. Then (1.1) is the heat equation on X . In this paper we'll look at the special case where X is a riemannian symmetric space of noncompact type. Thus X is a noncompact riemannian manifold with a very large symmetry group G, harmonic analysis on X is understood in terms of the s...

In this paper, we introduce a concept of B-minimal sub-manifolds and discuss the stability of such a sub-manifold in a Riemannian manifold (M, g). Assume B(x) is a smooth function on M . By definition, we call a sub-manifold Σ B-minimal in (M, g) if the product sub-manifold Σ × S1 is a minimal sub-manifold in a warped product Riemannian manifold (M×S1, g+ e2B(x)dt2), so its stability is closely...

The goal of the present paper is to analyze some geometric features Clairaut pointwise slant submersions whose total manifold a locally product Riemannian manifold. We describe from onto study by providing consequent which defines geodesics on space this type submersions. also give non-trivial example manifolds are Riemannian.

In pseudo-Riemannian geometry the spaces of space-like and timelike geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. We describe the geometry of these structures and their generaliza...

One of the most fundamental problems in submanifold theory is to establish simple relationships between intrinsic and extrinsic invariants of the submanifolds (cf. [6]). A general optimal inequality for submanifolds in Riemannian manifolds of constant sectional curvature was obtained in an earlier article [5]. In this article we extend this inequality to a general optimal inequality for arbitra...

In recent years, nonlinear dimensionality reduction (NLDR) techniques have attracted much attention in visual perception and many other areas of science. We propose an efficient algorithm called Riemannian manifold learning (RML). A Riemannian manifold can be constructed in the form of a simplicial complex, and thus its intrinsic dimension can be reliably estimated. Then the NLDR problem is sol...