Let Q be a symmetric bilinear form on R(n)=R(p+q+r) with corank r, rank p+q and signature type (p, q), p resp. q denoting positive resp. negative dimensions. We consider the degenerate spin group Spin(Q) = Spin(p, q, r) ...

Newton-Cartan manifolds and the Galilei group are defined by the use of co-rank one degenerate metric tensor. Newton-Cartan connection is lifted to the degenerate spinor bundle over a Newton-Cartan 4-manifold by the aid ...

We show that self-dual two-forms in 2n-dimensional spaces determine a n(2)-n+1-dimensional manifold S-2n and the dimension of the maximal linear subspaces of S-2n is equal To the (Radon-Hurwitz) number of linearly independent ...

It is well-known that a torsion-free linear connection on a light-like manifold (M, g) compatible with the degenerate metric g exists if and only if Rad(TM) is a Killing distribution. In case of existence, there is an ...

We construct a consistent set of monopole equations on eight-manifolds with Spin(7) holonomy. These equations are elliptic and admit non-trivial solutions including all the 4-dimensional Seiberg-Witten solutions as a special case.

We discuss the Seiberg-Witten theory in four dimensions and possible generalizations to eight dimensions. We propose an action which is minimized by a set of monopole equations, previously obtained as a generalization of ...

Bu tezde dejenere metrik tensörle donatılabilen türevlenebilir M manifoldlarıyla ilgilenilmiştir. Ko-rankı bir olan dejenere metrik tensör kullanılarak Newton-Cartan manifoldu, Newton-Cartan bağlantısı ve Galilei grubu ...

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Self-dual gauge fields in even dimensional spaces are characterised by a set of constraints on the eigenvalues of F. We derive a new topological bound (Latin small letter esh sign)M(F, F)2 ? ?M P12 on a compact 8-manifold ...

Let w be a 2-form on a 2n dimensional manifold. In previous work, we called w "strong self-dual, if the eigenvalues of its matrix with respect to an orthonormal frame are equal in absolute value. In a series of papers, we ...