On 4-dimensional, conformally flat, almost $\epsilon$-K\"ahlerian manifolds

TL;DR

This paper characterizes the local structure of 4-dimensional, conformally flat, almost psilon-Ke4hlerian manifolds using paraquaternionic functions, providing new insights into their geometric properties and examples.

Contribution

It introduces a novel characterization of these manifolds via paraquaternionic functions, expanding understanding of their structure and examples.

Findings

Characterization of local structure using paraquaternionic functions

Discussion of explicit examples of such manifolds

Extension of geometric understanding of conformally flat, almost psilon-Ke4hlerian manifolds

Abstract

The local structure of 4-dimensional, conformally flat, almost $\epsilon$-K\"ahlerian (i.e., almost pseudo-K\"ahlerian and almost para-K\"ahlerian) manifolds is characterized with the help of left-regular and right-regular paraquaternionic functions. Examples of such structures are discussed.