On nearly Sasakian and nearly cosymplectic manifolds

TL;DR

This paper proves that nearly Sasakian manifolds of dimension greater than five are actually Sasakian, and classifies nearly cosymplectic manifolds in higher dimensions, offering new insights into their geometric structure.

Contribution

It establishes that nearly Sasakian manifolds of dimension >5 are Sasakian and provides a classification for nearly cosymplectic manifolds in higher dimensions.

Findings

Nearly Sasakian manifolds of dimension >5 are Sasakian.

Classified nearly cosymplectic manifolds of dimension >5.

Provided new criteria for identifying Sasakian manifolds.

Abstract

We prove that every nearly Sasakian manifold of dimension greater than five is Sasakian. This provides a new criterion for an almost contact metric manifold to be Sasakian. Moreover, we classify nearly cosymplectic manifolds of dimension greater than five.