On deformations of G(2)-structures by Killing vector fields

ÖZDEMİR N., AKTAY Ş.

ADVANCES IN GEOMETRY, vol.14, no.4, pp.683-690, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 4
  • Publication Date: 2014
  • Doi Number: 10.1515/advgeom-2014-0012
  • Journal Name: ADVANCES IN GEOMETRY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.683-690
  • Keywords: G(2) structure, 3-Sasakian manifold, MANIFOLDS
  • Anadolu University Affiliated: Yes

Abstract

In this paper, vectorial type deformations of a 7-dimensional manifold with structure group G 2 are considered. The fundamental 3-form of such a manifold is deformed by a vector field, and the new cross product and the new Levi-Civita covariant derivation of the new metric are obtained in terms of the old ones. An example of a 7-dimensional manifold with structure group G 2 which is in the widest class W in the classification of Fernandez and Gray is given; this manifold has a nontrivial Killing vector field corresponding to the new metric.