On super generalized recurrent manifolds

TL;DR

This paper introduces the super generalized recurrent manifold, a new geometric structure that extends existing recurrent manifolds, and explores its properties with a concrete example.

Contribution

It proposes the super generalized recurrent manifold, unifying and extending previous notions, and studies its geometric properties with an explicit example.

Findings

Introduces super generalized recurrent manifold concept

Establishes geometric properties of the new structure

Provides an example demonstrating existence

Abstract

To generalize the notion of recurrent manifold, there are various recurrent like conditions in the literature. In this paper we present a recurrent like structure, namely, \textit{super generalized recurrent manifold}, which generalizes both the hyper generalized recurrent manifold and weakly generalized recurrent manifold. The main object of the present paper is to study the geometric properties of super generalized recurrent manifold. Finally to ensure the existence of such structure we present a proper example by a suitable metric.