# Methods of holonomy theory for Ricci‐flat Riemannian manifolds

@article{McInnes1991MethodsOH, title={Methods of holonomy theory for Ricci‐flat Riemannian manifolds}, author={Brett McInnes}, journal={Journal of Mathematical Physics}, year={1991}, volume={32}, pages={888-896} }

Compact, Ricci‐flat Riemannian manifolds often arise in physical applications, either as a technical device or as models of ‘‘internal’’ space. The idea of extending the holonomy group of such a manifold to a larger gauge group (‘‘embedding the connection in the gauge group’’) plays a fundamental role in the ‘‘manifold compactification’’ approach to superstring phenomenology, and the work of Gepner suggests that this idea may have equally fundamental analogs in other approaches. The holonomy…

## 18 Citations

Holonomy groups of compact Riemannian manifolds: A classification in dimensions up to ten

- Mathematics
- 1993

The possible holonomy groups of compact, locally irreducible Riemannian manifolds are studied. Motivated by applications arising in physics, it is not required that these manifolds be simply…

On Rigidly Scalar-Flat Manifolds

- Mathematics
- 1999

Witten and Yau (hep-th/9910245) have recently considered a generalisation of the AdS/CFT correspondence, and have shown that the relevant manifolds have certain physically desirable properties when…

Spin Holonomy of Einstein Manifolds

- Mathematics
- 1999

Abstract:Berger's Theorem classifies the linear holonomy groups of irreducible, simply connected Riemannian manifolds. For physical applications, however, it is at least as important to have a…

On the full holonomy group of Lorentzian manifolds

- Mathematics
- 2014

The classification of restricted holonomy groups of $$n$$n-dimensional Lorentzian manifolds was obtained about ten years ago. However, up to now, not much is known about the structure of the full…

Examples of Einstein manifolds with all possible holonomy groups in dimensions less than seven

- Mathematics
- 1993

In an earlier work, the possible holonomy groups of all compact locally irreducible Riemannian manifolds of dimensions up to ten were classified, placing particular emphasis on the…

Holonomy groups of Lorentzian manifolds

- Mathematics
- 2015

In this paper, a survey of the recent results about the classification of the connected holonomy groups of the Lorentzian manifolds is given. A simplification of the construction of the Lorentzian…

Global Aspects of Holonomy in Pseudo-Riemannian Geometry

- Mathematics
- 2011

A pseudo-Riemannian vector bundle (E, h,∇, π,X) is a smooth real vector bundle π : E → X with a bundle metric h of signature (r, s) on E and a metric connection ∇ on (E, h). Suppose the full holonomy…

How to Find the Holonomy Algebra of a Lorentzian Manifold

- Mathematics
- 2011

AbstractManifolds with exceptional holonomy play an important role in string theory, supergravity and M-theory. It is explained how one can find the holonomy algebra of an arbitrary Riemannian or…

The quotient construction for a class of compact Einstein manifolds

- Mathematics
- 1993

Given any Einstein manifoldME, one can obtain further examples of Einstein manifolds by taking the quotientME/G by a freely acting, properly discontinuous group of isometries. We study this method in…

N ov 1 99 9 On Rigidly Scalar-Flat Manifolds

- Mathematics
- 1999

Witten and Yau (hep-th/9910245) have recently considered a generalisation of the AdS/CFT correspondence, and have shown that the relevant manifolds have certain physically desirable properties when…

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