Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Einstein metrics on conformal products

Andrei Moroianu, Mihaela Pilca

Abstract

We show that under some natural geometric assumption, Einstein metrics on conformal products of two compact conformal manifolds are warped product metrics.

Einstein metrics on conformal products

Abstract

We show that under some natural geometric assumption, Einstein metrics on conformal products of two compact conformal manifolds are warped product metrics.
Paper Structure (7 sections, 8 theorems, 65 equations)

This paper contains 7 sections, 8 theorems, 65 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Weyl connections
  4. Differential operators on products
  5. Conformal product structures
  6. Curvature of conformal product metrics
  7. Main Result

Key Result

Theorem 1.1

Let $(M_1,c_1)$ and $(M_2,c_2)$ by two compact conformal manifolds such that $\mathrm{dim}(M_1\times M_2)\geq 3$ and let $c$ be a conformal product structure on $M_1\times M_2$, with adapted Weyl connection $\nabla$. Assume that $c$ contains an Einstein metric $g$, such that the restriction to $\mat

Theorems & Definitions (17)

  • Theorem 1.1
  • Lemma 2.1
  • proof
  • Definition 2.2
  • Definition 2.3
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • Lemma 2.6
  • ...and 7 more