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Randers Ricci soliton homogeneous nilmanifolds

Hamid Reza Salimi Moghaddam

Abstract

Let $F$ be a left invariant Randers metric on a simply connected nilpotent Lie group $N$, induced by a left invariant Riemannian metric ${\hat{\textbf{\textit{a}}}}$ and a vector field $X$ which is $I_{\hat{\textbf{\textit{a}}}}(M)$-invariant. If the Ricci flow equation has a unique solution then, $(N,F)$ is a Ricci soliton if and only if $(N,F)$ is a semialgebraic Ricci soliton.

Randers Ricci soliton homogeneous nilmanifolds

Abstract

Let be a left invariant Randers metric on a simply connected nilpotent Lie group , induced by a left invariant Riemannian metric and a vector field which is -invariant. If the Ricci flow equation has a unique solution then, is a Ricci soliton if and only if is a semialgebraic Ricci soliton.

Paper Structure

This paper contains 3 sections, 6 theorems, 32 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Results

Key Result

Theorem 2.2

(see Bao-Chern-Shen) Suppose that $(M,F)$ is a Finsler manifold. The pull-back bundle $\pi^\ast TM$ admits a unique torsion free linear connection $\nabla$, called the Chern connection, which is almost g-compatible. The coefficients of the connection are of the form where $\frac{\delta}{\delta x^j}:=\frac{\partial}{\partial x^j}-N^i_j\frac{\partial}{\partial y^i}$.

Theorems & Definitions (15)

  • Definition 2.1
  • Theorem 2.2
  • Definition 2.3
  • Definition 3.1
  • Remark 3.2
  • Proposition 3.3
  • Remark 3.4
  • Proposition 3.5
  • proof
  • Corollary 3.6
  • ...and 5 more