On the Curvature Properties of Manifolds with Deformed $G_2$ Structures

N. Ozdemir, S. Aktay

Anadolu University, Turkey

Abstract: In this paper, we study the curvature properties of a manifold with structure group $G_2$ whose fundamental 3-form is deformed by a Killing vector field of unit length. We obtain some results concerning conditions under which this manifold is flat, Einstein, or isometric to the unit sphere.

Keywords: $G_2$-structure, curvature.

UDC: 514

Received: 10.03.2015

DOI: 10.4213/mzm11912

 English version: Mathematical Notes, 2018, 103:3, 447–452

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