Isotropic Riemannian Maps and Helices along Riemannian Maps

TL;DR

This paper introduces isotropic Riemannian maps as a generalization of isotropic immersions and explores the properties of helices along Riemannian maps, providing new characterizations and examples.

Contribution

It defines isotropic Riemannian maps, offers a characterization, and studies the transportation of helices along these maps, extending the understanding of geometric structures in Riemannian geometry.

Findings

Defined isotropic Riemannian maps and provided an example.

Characterized the transportation of helices along Riemannian maps.

Extended the theory of helices in the context of Riemannian maps.

Abstract

This work has two main purposes. The first aim is to study isotropic Riemannian maps as a generalization of isotropic immersions. For this purpose, the concept of isotropic Riemannian map is presented, an example is given and a characterization is obtained. The second aim is to study the helices along Riemannian map. For this purpose, by using the notion of isotropic Riemannian map and the notion of helix on the manifold, a characterization is obtained for the transportation of a helix on the total manifold to the target manifold along a Riemannian map.