On a class of immersions between almost para-Hermitian manifolds

TL;DR

This paper studies a special class of immersions called slant submanifolds in almost para-Hermitian manifolds, classifying certain pointwise slant surfaces in four-dimensional cases, extending concepts from Hermitian geometry.

Contribution

It introduces and classifies pointwise slant surfaces within four-dimensional almost para-Hermitian manifolds, expanding the understanding of submanifold geometry in this setting.

Findings

Classification of pointwise slant surfaces in four-dimensional manifolds

Extension of slant submanifold concept to para-Hermitian geometry

Identification of properties of immersions in this context

Abstract

Almost para-Hermitian manifold it is manifold equipped with almost para-complex structure and compatible pseudo-metric of neutral signature. It is considered a class of immersions of almost para-Hermitian manifolds into almost para-Hermitian manifolds. Such immersions are called slant submanifolds. The concept is an analogue of the idea of slant submanifold in almost Hermitian geometry. There are classified pointwise slant surfaces of four dimensional almost para-Hermitian manifold.