On isometric and minimal isometric embeddings

TL;DR

This paper investigates isometric and minimal isometric embeddings of quasi-$k$-curved Riemannian metrics, extending space form metrics, with explicit examples and results on their existence and rigidity.

Contribution

It introduces quasi-$k$-curved metrics, generalizes space form metrics, and provides new existence and rigidity results for their isometric embeddings.

Findings

Constructed explicit examples of embeddings.

Proved existence results for quasi-$k$-curved metrics.

Established rigidity properties of these embeddings.

Abstract

In this paper we study critial isometric and minimal isometric embeddings of classes of Riemannian metrics which we call {\it quasi-$k$-curved metrics}. Quasi-$k$-curved metrics generalize the metrics of space forms. We construct explicit examples and prove results about existence and rigidity.