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arXiv · 1601.07500

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

Rebecca Glover·Sema Salur
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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.

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Rebecca Glover, Sema Salur. 2016-01-27. Lagrangian-type submanifolds of Spin(7) manifolds and their deformations. https://arxiv.org/abs/1601.07500

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