Bibliography: p. 188-201.
|Series||Pitman research notes in mathematics series,, 201|
|LC Classifications||QA649 .S27 1989|
|The Physical Object|
|Pagination||201 p. :|
|Number of Pages||201|
|LC Control Number||88008414|
Lecture notes for the minicourse "Holonomy Groups in Riemannian geometry", a part of the XVII Brazilian School of Geometry, to be held at UFAM . Parallel transport and holonomy groups Let M be a manifold, E! M a vector bundle over M, and rE a connection on E. Let °: [0;1]! M be a smooth curve in M. Then the pull-back °⁄(E) of E to [0;1] is a vector bundle over [0;1] with ﬂbre E°(t) over t 2 [0;1], where Ex is the ﬂbre of E over x 2 M. The connection rE pulls back under. Topics covered are: Classification of pseudo-Riemannian symmetric spaces Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential. Riemannian holonomy groups and calibrated geometry covers an exciting and active area of research at the crossroads of several different fields in Mathematics and Physics. Drawing on the author's previous work the text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.
Riemannian Holonomy and Algebraic Geometry Arnaud BEAUVILLE Version (25/1/99) Introduction This survey is devoted to a particular instance of the interaction between Riemannian geometry and algebraic geometry, the study of manifolds with special holonomy. The holonomy group is one of the most basic objects associated with. Riemannian, Symplectic and Weak Holonomy Article (PDF Available) in Annals of Global Analysis and Geometry 18(3) August with 73 Reads How we measure 'reads'. Riemannian Holonomy Groups and Calibrated Geometry by Dominic David Joyce, , available at Book Depository with free delivery : Dominic David Joyce. Riemannian Holonomy Groups and Calibrated Geometry Dominic D. Joyce This graduate level text covers an exciting and active area of research at the crossroads of several different fields .
The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and K hler geometry. Then the Calabi conjecture is proved and used to deduce the existence of compact manifolds with holonomy SU(m) (Calabi-Yau manifolds) and Sp(m) (hyperk hler manifolds).Cited by: Another textbook about Riemannian holonomy groups by S. M. Salamon [Riemannian geometry and holonomy groups, Longman Sci. Tech., Harlow, ] was the standard reference for a long time. It is still very much worthwhile, although its approach tends to be more representation-theoretic, and the present book stresses a differential-geometric and. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie . Holonomy groups in Riemannian geometry Lecture 4 Novem SubmanifoldsG-actionsBerger ThmHolonomy and cohomology Equivalent formulation of the Berger theorem By inspection, each group in Berger’s list acts transitively on the unit sphere. On the other hand, all groups acting transitively on.