On seven dimensional 3-Sasakian manifolds

Özdemi̇r Nilüfer

doi:10.1501/commua1_0000000748

Abstract

3-Sasakian manifolds in dimension seven have cocalibrated andnearly parallel G-structures. In this work, cocalibrated G-structure is deformed by one of the characteristic vector fields of the 3-Sasakian structure anda new G2structure is obtained whose metric has negative scalar curvature. Inaddition, the new G2structure has a nonzero Killing vector field. Then, by using this deformation, new covariant derivative on the spinor bundle is obtained and the new Dirac operator is written in terms of the Dirac operator before deformation

Highlights

There exist several deformations of G2 structures to obtain new G2 structures
The new G2 structure has a nonzero Killing vector ...eld. By using this deformation, new covariant derivative on the spinor bundle is obtained and the new Dirac operator is written in terms of the Dirac operator before deformation
It is shown that seven dimensional 3-Sasakian manifolds have a coclosed and nearly parallel G2-structures in [8]

Summary

INTRODUCTION

There exist several deformations of G2 structures to obtain new G2 structures. Some of them are conformal deformations which are extensively studied in [1, 2]. Other types of deformations use vector ...elds to get new G2 structures [2]. Relations between the spectral properties of Dirac operator and seven dimensional 3-Sasakian manifolds are investigated by [5, 6, 7]. It is shown that seven dimensional 3-Sasakian manifolds have a coclosed and nearly parallel G2-structures in [8]. To obtain a new G2-structure from a ...xed G2-structure, one of the characteristic vector ...elds of the 3-Sasakian structure is used for changing the fundamental 3-form

PRELIMINARIES

VECTORIAL TYPE DEFORMATION OF RIEMANNIAN MANIFOLDS WITH STRUCTURE GROUP G2

DIRAC OPERATOR ON SEVEN DIMENSIONAL 3-SASAKIAN MANIFOLDS