Quasi-isometry between two almost contact metric manifolds

TL;DR

This paper introduces the concept of quasi-isometry between almost contact metric manifolds, explores curvature properties, provides an example involving Sasakian structures, and relates scalar curvature to quasi-isometric constants.

Contribution

It extends the notion of quasi-isometry to almost contact metric manifolds and investigates their curvature properties and scalar curvature relations.

Findings

Curvature properties of quasi-isometrically embedded manifolds are characterized.

An explicit example of quasi-isometry between Sasakian structures is constructed.

A relation between scalar curvature and quasi-isometric constants is established.

Abstract

In this paper the notion of quasi-isometry between two Riemannian manifolds has been introduced. This idea is also imposed to study quasi-isometry between two almost contact metric manifolds. Moving further, some curvature properties of two quasi-isometrically embedded almost contact metric manifolds, $N(k)-$contact metric manifolds and Sasakian manifolds are investigated. Next, an illustrative example of a quasi-isometry between two Sasakian structures is constructed. Finally, a relation between the scalar curvature and the quasi-isometric constants for two quasi-isometric Riemannian manifolds has been established.