English

Lagrangian-type submanifolds of Spin(7) manifolds and their deformations

Differential Geometry 2016-01-28 v1 Geometric Topology

Abstract

In an earlier paper we showed that the space of deformations of a smooth, compact, orientable Harvey-Lawson submanifold HL in a G2 manifold M can be identified with the direct sum of the space of smooth functions and closed 2-forms on HL. In that paper, we also introduced a new class of Lagrangian-type 4-dimensional submanifolds inside G2 manifolds, called them RS submanifolds, and proved that the space of deformations of a smooth, compact, orientable RS submanifold in a G2 manifold M can be identified with closed 3-forms on RS. In this short note, we define a new class of Lagrangian-type 4-dimensional submanifolds inside Spin(7) manifolds, which we call L-submanifolds. We show that the space of deformations of a smooth, compact, orientable L-submanifold in a Spin(7) manifold N can be identified with the space of closed 3-forms on L.

Keywords

Cite

@article{arxiv.1601.07500,
  title  = {Lagrangian-type submanifolds of Spin(7) manifolds and their deformations},
  author = {Rebecca Glover and Sema Salur},
  journal= {arXiv preprint arXiv:1601.07500},
  year   = {2016}
}

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6 pages