Super warped products with a semi-symmetric non-metric connection

TL;DR

This paper introduces a semi-symmetric non-metric connection on super Riemannian manifolds, computes related curvature tensors, and explores conditions under which these spaces are Einstein super spaces, expanding geometric understanding in supergeometry.

Contribution

It defines a new type of connection on super Riemannian manifolds and analyzes its curvature properties and Einstein conditions in super warped product spaces.

Findings

Computed curvature and Ricci tensors for the new connection

Established conditions for super warped products to be Einstein super spaces

Introduced two types of super warped product spaces with this connection

Abstract

In this paper, we define a semi-symmetric non-metric connection on super Riemannian manifolds. And we compute the curvature tensor and the Ricci tensor of a semi-symmetric non-metric connection on super warped product spaces. Next, we introduce two kinds of super warped product spaces with a semi-symmetric non-metric connection and give the conditions that two super warped product spaces with a semi-symmetric non-metric connection are the Einstein super spaces with a semi-symmetric non-metric connection.