On Douglas warped product metrics

TL;DR

This paper investigates a new class of warped metrics with vanishing Douglas curvature, providing a complete classification and revealing the equivalence of Landsberg and Berwald warped product metrics, along with examples.

Contribution

It derives the differential equation for Douglas warped product metrics and classifies all such metrics, including Ricci-flat cases, establishing their properties and examples.

Findings

All Douglas warped product metrics are characterized by a specific differential equation.

Landsberg and Berwald warped product metrics are shown to be equivalent.

The paper classifies Douglas Ricci-flat warped product metrics.

Abstract

We study the new warped metric proposed by P. Marcal and Z. Shen. We obtain the differential equation of such metrics with vanishing Douglas curvature. By solving this equation, we obtain all Douglas warped product metrics. We show that Landsberg and Berwald warped product metrics are equivalent. We classify Douglas Ricci-flat metrics. Examples are included.