(a, 1)f structures on product of spheres

TL;DR

This paper constructs examples of $(a, 1)f$ Riemannian structures, generalizing $r$-paracontact structures, on products of spheres with codimension 1 or 2 in Euclidean spaces.

Contribution

It provides explicit examples of $(a, 1)f$ structures on product spheres, extending the understanding of such geometric structures in differential geometry.

Findings

Examples of $(a, 1)f$ structures on product spheres are constructed.

The structures generalize $r$-paracontact structures.

Applications to geometric analysis of product manifolds.

Abstract

Our aim in this paper is to give some examples of $(a, 1)f$ Riemannian structures (a generalization of an $r$-paracontact structure) induced on product of spheres of codimension $r$ ($r \in \{1,2\} $) in an $m$-dimensional Euclidean space ($m>2$), endowed with an almost product structure.