Doubly Extended Lie Groups - Curvature, Holonomy and Parallel Spinors
نویسنده
چکیده
In the present paper we study the geometry of doubly extended Lie groups with their natural biinvariant metric. We describe the curvature, the holonomy and the space of parallel spinors. This is completely done for all simply connected groups with biinvariant metric of Lorentzian signature (1, n − 1), of signature (2, n − 2) and of signature (p, q), where p + q ≤ 6. Furthermore, some special series with higher signature are discussed.
منابع مشابه
On the stability of Riemannian manifold with parallel spinors
Inspired by the recent work [HHM03], we prove two stability results for compact Riemannian manifolds with nonzero parallel spinors. Our first result says that Ricci flat metrics which also admit nonzero parallel spinors are stable (in the direction of changes in conformal structures) as the critical points of the total scalar curvature functional. Our second result, which is a local version of ...
متن کاملParallel spinors and holonomy groups on pseudo-Riemannian spin manifolds
We describe the possible holonomy groups of simply connected irreducible non-locally symmetric pseudo-Riemannian spin manifolds which admit parallel spinors.
متن کاملConformal Killing Spinors and the Holonomy Problem in Lorentzian Geometry – a Survey of New Results –
This paper is a survey of recent results about conformal Killing spinors in Lorentzian geometry based on a lecture given during the Summer Program Symmetries and Overdetermined Systems of Partial Differential Equations at IMA, Minnesota, 17.07.06 04.08.06. In particular, we will focus on a special class of geometries admitting conformal Killing spinors – on Brinkmann spaces with parallel spinor...
متن کاملThe Spinorial Geometry of Supersymmetric Heterotic String Backgrounds
We determine the geometry of supersymmetric heterotic string backgrounds for which all parallel spinors with respect to the connection ∇̂ with torsion H , the NS⊗NS three-form field strength, are Killing. We find that there are two classes of such backgrounds, the null and the timelike. The Killing spinors of the null backgrounds have stability subgroups K ⋉R 8 in Spin(9, 1), for K = Spin(7), SU...
متن کاملOn Parallel Transport and Curvature —— Graduate Project
Given connection ∇ on a smooth vector bundle E → M , with connected base space M , the set of the parallel transport maps (associated to ∇) along closed loops based at x ∈M form a subgroup, Hol(∇), of the general linear group on the fibre Ex, GL(Ex). The group Hol(∇) is known as the holonomy group of the connection and it is independent of the base point x under conjugation of elements of the g...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002