Basic Albanese maps of regular Riemannian foliations

TL;DR

This paper introduces the basic Albanese map for foliated Riemannian manifolds, relating it to classical Albanese maps and exploring its properties through key examples.

Contribution

It defines the basic Albanese map for foliated Riemannian manifolds using basic 1-forms and connects it to classical Albanese maps, providing new insights.

Findings

Establishment of the basic Albanese map concept for foliated manifolds

Relation between basic Albanese map and classical Albanese map

Analysis of properties through important examples

Abstract

In the paper we introduce the notion of basic Albanese map which we define for foliated Riemannian manifolds using basic 1-forms. We relate this mapping to the classical Albanese map for the ambient manifold. The study of general properties is supplemented with the description of several important examples.