Tangent Bundles with Sasaki Metric and Almost Hypercomplex Pseudo-Hermitian Structure

TL;DR

This paper studies tangent bundles endowed with a specific geometric structure combining almost hypercomplex and pseudo-Hermitian properties, providing classifications and explicit 8-dimensional examples.

Contribution

It introduces a classification of tangent bundles with these structures and constructs explicit 8-dimensional examples from known cases.

Findings

Classification of tangent bundles with almost hypercomplex pseudo-Hermitian structures

Explicit 8-dimensional examples derived from known manifolds

Characterization within relevant geometric categories

Abstract

The tangent bundle as a $4n$-manifold is equipped with an almost hypercomplex pseudo-Hermitian structure and it is characterized with respect to the relevant classifications. A number of 8-dimensional examples of the considered type of manifold are received from the known explicit examples in that manner.