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