Please use this identifier to cite or link to this item:
Title: Holonomy groups and holonomy representations
Authors: McInnes, B. 
Issue Date: 1995
Citation: McInnes, B. (1995). Holonomy groups and holonomy representations. Journal of Mathematical Physics 36 (8) : 4450-4460. ScholarBank@NUS Repository.
Abstract: The holonomy group of a Riemannian manifold always arises in geometry through a particular representation, not as an abstract group. One can therefore ask whether there exist pairs of (compact, locally irreducible) manifolds with holonomy groups which are isomorphic, yet distinct, because the holonomy representations are not equivalent. A theorem of Besse asserts that this is not possible in the simply connected case; however, it is possible for certain nonsimply connected manifolds. Here we identify all of these manifolds (up to space form problems) hi the case where the Ricci curvature is not negative. This allows us to solve the holonomy classification problem for all compact, locally irreducible Riemannian manifolds of positive Ricci curvature. © 1995 American Institute of Physics.
Source Title: Journal of Mathematical Physics
ISSN: 00222488
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

Page view(s)

checked on Aug 10, 2018

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.