Abstract
In this work, we systematically analyze supersymmetry on solvable Lorentzian symmetric spaces. We provide explicit conditions under which spinor connections admit supersymmetry by describing the underlying Lie bracket structure. We introduce the necessary notions and tools for flat connections and, on this basis, establish that in all dimensions up to eleven, nontrivial and at most canonically restricted irreducible supersymmetries exist. Moreover, we extend the examples known from the literature to a complete classification and supplement it with a full catalogue of N=2 extended natural supersymmetries.
By presenting further examples—including cases with N>2, non-natural, non-canonically restricted, and non-flat supersymmetries—we illustrate how our framework applies to the general situation. In particular, we demonstrate that in any dimension admitting an irreducible super extension, a nontrivial 3/4-restricted supersymmetry is possible.
Abstract
In this thesis, we combine the notions of supergeometry with supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo-)Riemannian manifolds, thereby allowing vector fields and spinor fields to be treated as equivalent geometric objects. This serves as the starting point for our definition of supersymmetric Killing structures.
The latter combines subspaces of vector fields and spinor fields, provided they satisfy certain field equations. This naturally leads to a superalgebra that extends the supersymmetry algebra to the setting of non-flat reduced spaces.
We examine in detail the additional terms that arise in this structure, the so-called center of the supersymmetric Killing structure. Furthermore, we provide numerous examples, emphasizing those in which the center takes a particularly simple form.
Abstract
In the first part of the thesis, the various concepts of connections in differential geometry are examined. It is shown that connections on manifolds and on vector bundles are in one-to-one correspondence with those on principal bundles.
The second part focuses on a special class of connections: the self-dual connections on SU(2)-principal bundles over the four-sphere S4 with integral second Chern class c2=−k. These are the k-instantons.
Abstract
Wir präsentieren hier einen Vorschlag für eine motivierende Einführung in die Volumenberechnung mit Integralen sowie in die Theorie der Quadraturformeln. Der Übergang zwischen beiden Schwerpunkten erfolgt durch eine ausführliche Diskussion der Keplerschen Fassregel.
Abstract
We present here a complete list of quadratic Poisson structures in dimension four. For details on the decomposition of quadratic Poisson structures see the related paper.
Abstract
We use the notations introduced in [F. Klinker: Supersymmetric Killing Structures] to explain how we derive the signs. The calculations are an extended version of the calculations for the Lorentzian case which have their origin in [J. Scherk: Extended supersymmetry and extended supergravity theories].
Abstract
In this note, we compare the spinor bundle of a Riemannian manifold with the spinor bundles of the Riemannian factors.