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A note on gradient Solitons on two classes of almost Kenmotsu Manifolds

Krishnendu De, Uday Chand De

Abstract

The purpose of the article is to characterize \textbf{gradient $(m,ρ)$-quasi Einstein solitons} within the framework of two classes of almost Kenmotsu Manifolds. Finally, we consider an example to justify a result of our paper.

A note on gradient Solitons on two classes of almost Kenmotsu Manifolds

Abstract

The purpose of the article is to characterize \textbf{gradient -quasi Einstein solitons} within the framework of two classes of almost Kenmotsu Manifolds. Finally, we consider an example to justify a result of our paper.

Paper Structure

This paper contains 10 sections, 6 theorems, 69 equations.

Table of Contents

  1. Introduction
  2. Almost Kenmotsu manifolds
  3. Gradient $(m,\rho)$-quasi Einstein solitons on a $(2n+1)$-dimensional almost Kenmotsu manifold
  4. Gradient $(m,\rho)$-quasi Einstein solitons on a $3$-dimensional Kenmotsu manifold
  5. Example
  6. Declarations
  7. Funding
  8. Conflicts of interest/Competing interests
  9. Availability of data and material
  10. Code availability

Key Result

Lemma 2.1

(Lemma. 3.2 of wal) Let $(M^{2n+1},\eta,\xi,\phi,g)$ be an almost Kenmotsu manifold such that $\xi$ belongs to the $(k,\mu)'$-nullity distribution and $h'\neq0$. Then the Ricci operator $Q$ of $M^{2n+1}$ is given by where $k < -1$, moreover, the scalar curvature of $M^{2n+1}$ is $2n(k-2n)$.

Theorems & Definitions (7)

  • Lemma 2.1
  • Theorem 3.1
  • Corollary 3.2
  • Remark 3.3
  • Lemma 4.1
  • Theorem 4.2
  • Corollary 4.3