Bochner and Conformal Flatness of Normal Metric Contact Pairs

TL;DR

This paper classifies certain geometric structures called normal metric contact pairs, showing they are locally isometric to Hopf manifolds under specific flatness conditions, and extends this to classify related Vaisman manifolds.

Contribution

It provides a classification of normal metric contact pairs with flatness conditions, linking them to Hopf manifolds and extending to Vaisman manifolds.

Findings

Normal metric contact pairs with Bochner or conformal flatness are locally isometric to Hopf manifolds.

Classification of locally conformally flat non-Kähler Vaisman manifolds.

Establishment of geometric conditions leading to the classification.

Abstract

We prove that the normal metric contact pairs with orthogonal characteristic foliations, which are either Bochner flat or locally conformally flat, are locally isometric to the Hopf manifolds. As a corollary we obtain the classification of locally conformally flat and Bochner-flat non-K\"ahler Vaisman manifolds.