Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On Locally Conformal Spin(7) Structure

Eyup Yalcinkaya

Abstract

This article reveals a significant connection in geometry: when the Lee form $θ$ is normal to an almost Hermitian manifold $N$, it implies that $N$ possesses a nearly Kähler structure. Investigating locally conformally Spin(7) manifolds with 2-vector fields, our study provides a concise yet rigorous proof of this relationship.

On Locally Conformal Spin(7) Structure

Abstract

This article reveals a significant connection in geometry: when the Lee form is normal to an almost Hermitian manifold , it implies that possesses a nearly Kähler structure. Investigating locally conformally Spin(7) manifolds with 2-vector fields, our study provides a concise yet rigorous proof of this relationship.
Paper Structure (5 sections, 9 theorems, 17 equations)

This paper contains 5 sections, 9 theorems, 17 equations.

Table of Contents

  1. History
  2. Introduction
  3. $Spin(7$)-structures
  4. LCSpin(7)-structure with a vector field
  5. LCSpin(7)-structure with 2-vector fields

Key Result

Theorem 3.2

(Lawson) Let $M$ be a differentiable 8-manifold. $M$ admits a $Spin(7)$-structure if and only if $w_1(M)=w_2(M)=0$ and for appropriate choice of orientation on $M$ we have that

Theorems & Definitions (13)

  • Definition 3.1
  • Theorem 3.2
  • Corollary 3.3
  • Definition 3.4
  • Theorem 4.1
  • Theorem 4.2
  • Theorem
  • Theorem
  • Theorem
  • Proposition 5.1
  • ...and 3 more