We study deformations of associative submanifolds of a G 2 manifold. We show that deformation spaces can be perturbed to be smooth and finite dimensional , and they can be made compact by constraining them with an additional equation and reducing it to Seiberg-Witten theory. This allows us to associate in-variants of certain associative submanifolds. More generally we apply this process to cert...

We study deformations of associative submanifolds Y 3 ⊂ M 7 of a G 2 manifold M 7. We show that the deformation space can be perturbed to be smooth, and it can be made compact and zero dimensional by constraining it with an additional equation. This allows us to associate local invariants to associative submanifolds of M. The local equations at each associative Y are restrictions of a global eq...

For any subgroup G ⊆ O(n), define a G-manifold to be an n-dimensional Riemannian manifold whose holonomy group is contained in G. Then a G-manifold where G is the Standard Model gauge group is precisely a Calabi–Yau manifold of 10 real dimensions whose tangent spaces split into orthogonal 4and 6-dimensional subspaces, each preserved by the complex structure and parallel transport. In particular...

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...

In this article we consider a closed Riemannian manifold (M, g) and A a subset of M. The purpose of this article is the comparison between the eigenvalues (λk(M))k≥1 of a Schrödinger operator P := −∆g + V on the manifold (M, g) and the eigenvalues (λk(M− A))k≥1 of P on the manifold (M− A, g) with Dirichlet boundary conditions.

Suppose M is a topological m-manifold, X is a generalized nmanifold satisfying the disjoint disks property (DDP ), m > n ≥ 5, f : M → X is an approximate fibration, with fiber the shape of a closed topological manifold F , and Y is a closed, 1-LCC, codimension three subset of X. We examine conditions under which f is controlled homeomorphic to an approximate fibration g : M → X such that g|g−1(...