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On geometry of the (generalized) G2 -manifolds

Jun 29, 2015
33 pages
Published in:
  • Int.J.Mod.Phys.A 30 (2015) 20, 1550112
  • Published: Jun 29, 2015
DOI:
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Abstract: (World Scientific)
In this paper, we first understand the classical G2-structure and G2-geometry from the viewpoint of spinor, which is a more familiar framework for physicists. Explicit construction of invariant spinor is given via the Dirac gamma matrices. We introduce a notion of multispinor bundle associated with invariant spinor and differential operator on the section of this bundle. Then we study the vector fields satisfy some additional properties on G2-manifold, more precisely, we prove some no-go theorems corresponding to the vector field preserving the associated 4-form on G2-manifold, and we also consider the nowhere-vanishing vector field which induces an integrable complex structure on the vertical direction of tangent bundle. Next we discuss the relation between the variation of metric and that of effective action on the moduli space of integrable G2-structures. In the last section, we deal with the structure operators on generalized G2-manifold after describing the integrability of generalized G2-structure, some identities of structure operators are derived, which are analogues of Kähler-type and Weitzenböck-type identities under the classical case. And finally, we introduce a flow of which a generalized G2-manifold can be realized as the fixed point.
  • (Generalized) G2 -manifolds
  • (bi)spinors
  • moduli space
  • structure operators