The L-sectional curvature of S-manifolds

TL;DR

This paper studies the L-sectional curvature of S-manifolds under various connections, providing conditions for constant curvature and calculating scalar curvature, with examples illustrating these cases.

Contribution

It introduces new conditions for constant L-sectional curvature in S-manifolds and computes scalar curvature for these cases, expanding understanding of their geometric properties.

Findings

Conditions for constant L-sectional curvature are established.

Scalar curvature is explicitly calculated in different cases.

Examples of S-manifolds satisfying these conditions are provided.

Abstract

We investigate L-sectional curvature of S-manifolds with respect to the Rieman- nian connection and to certain semi-symmetric metric and non-metric connections naturally related with the structure, obtaining conditions for them to be constant and giving examples of S-manifolds in such conditions. Moreover, we calculate the scalar curvature in all the cases.