A-manifolds on a principal torus bundle over an A-manifold base

TL;DR

This paper constructs new examples of A-manifolds, which are manifolds with cyclic-parallel Ricci tensor, by using a principal torus bundle over a product of almost Hodge A-manifolds, expanding the known classes of such manifolds.

Contribution

It introduces a novel method to generate A-manifolds on torus bundles over almost Hodge A-manifolds, enriching the geometric structures available in differential geometry.

Findings

New examples of A-manifolds constructed on torus bundles.

Demonstration of cyclic-parallel Ricci tensor properties in these manifolds.

Extension of known classes of A-manifolds through bundle constructions.

Abstract

We construct new examples of manifolds with cyclic-parallel Ricci tensor, so called A-manifolds, on a r-torus bundle over a product of almost Hodge A-manifolds.