A new class of metric f-manifolds

TL;DR

This paper introduces a new broad class of metric f-manifolds called (nearly) trans-S-manifolds, unifying several previously studied manifold types and exploring their properties with numerous examples.

Contribution

The paper defines (nearly) trans-S-manifolds, a new class that generalizes existing manifold types, and investigates their fundamental properties and examples.

Findings

Includes S-, C-, s-th Sasakian, and generalized Kenmotsu manifolds

Proves main properties of (nearly) trans-S-manifolds

Provides numerous illustrative examples

Abstract

We introduce a new general class of metric f-manifolds which we call (nearly) trans-S-manifolds and includes S- manifolds, C-manifolds, s-th Sasakian manifolds and generalized Kenmotsu manifold studied previously. We prove their main properties and we present many examples which justify their study.