arXiv subjects

Rebecca Glover

Publications and source records attributed to Rebecca Glover.

3 recordsLinked to original sources

arXiv2016

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

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.

math.DG↗

arXiv2015

Deformations of Lagrangian Type Submanifolds inside G2 manifolds

3-dimensional Harvey Lawson submanifolds were introduced in an earlier paper by Akbulut-Salur, as examples of Lagrangian-type manifolds inside G2 manifold. In this paper, we first show 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. We then introduce a new class of Lagrangian-type 4-dimensional submanifolds inside G2, call them RS submanifolds and prove 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.

math.GT↗

arXiv2013

Generalized twistor spaces for hyperkähler manifolds

Let M be a hyperkähler manifold. The S^2-family of complex structures compatible with the hyperkähler metric can be assembled into a single complex structure on Z=MxS^2; the resulting complex manifold is known as the twistor space of M. We describe the analogous construction for generalized complex structures in the sense of Hitchin. Specifically, we exhibit a natural S^2xS^2-family of generalized complex structures compatible with the hyperkähler metric, and assemble them into a single generalized complex structure on X=MxS^2xS^2. We call the resulting generalized complex manifold the generalized twistor space of M.

math.DG↗