Submanifolds in manifolds with metric mixed 3-structures

TL;DR

This paper investigates the geometry of invariant and anti-invariant submanifolds within manifolds equipped with mixed 3-structures, focusing on their properties in mixed 3-Sasakian and mixed 3-cosymplectic ambient spaces.

Contribution

It provides a detailed study of submanifolds in mixed 3-structured manifolds, highlighting their characteristics in specific geometric contexts.

Findings

Characterization of invariant submanifolds

Properties of anti-invariant submanifolds

Differences between mixed 3-Sasakian and mixed 3-cosymplectic cases

Abstract

Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a manifold endowed with a mixed 3-structure and a compatible (semi-Riemannian) metric. Particular attention is given to two cases of ambient space: mixed 3-Sasakian and mixed 3-cosymplectic.