On special submanifolds of the Page space

TL;DR

This paper investigates totally geodesic submanifolds within the Page space, analyzing their curvature properties and relationships to other metrics, revealing insights into their geometric structure.

Contribution

It introduces new classes of totally geodesic submanifolds in the Page space and explores their curvature and connections to other metrics.

Findings

Some submanifolds are constant curvature spaces

Curvature computations for various submanifolds

Relations between Page space and other metrics

Abstract

In this paper, we study some classes of submanifolds of codimension one and two in the Page space. These submanifolds are totally geodesic. We also compute their curvature and show that some of them are constant curvature spaces. Finally we give information on how the Page space is related to some other metrics on the same underlying smooth manifold.