Gauge field theory and complex geometry. Transl. from the Russian by N. Koblitz and J. R. King. With an appendix by S. Merkulov. 2nd ed. (English) Zbl 0884.53002

Manin, Yuri I.

Grundlehren der Mathematischen Wissenschaften. 289. Berlin: Springer. xii, 346 p. (1997).

This is the second edition of this valued monograph. It contains an Addendrum by S. Merkulov. In the first part of this Addendum he gives a survey of recent developments in twistor theory. In the second part, devoted to the theory of supermanifolds, two classes of examples are studied. The first one is the class of Riemannian supermanifolds in 3/2 dimensions. The second one is the classes of quaternionic supermanifolds in \(4k/2k+2\) dimensions.
This gives more illustrations of the general machinery developed in the main part of this book, which has been reviewed in Zbl 0576.53002 and Zbl 0641.53001.

Reviewer: S.M.Ivashkovich (Villeneuve d’Ascq)

MSC:

53-02	Research exposition (monographs, survey articles) pertaining to differential geometry
58-02	Research exposition (monographs, survey articles) pertaining to global analysis
53Z05	Applications of differential geometry to physics
32L25	Twistor theory, double fibrations (complex-analytic aspects)
53C07	Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
81T13	Yang-Mills and other gauge theories in quantum field theory
32-02	Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces
58J90	Applications of PDEs on manifolds
81-02	Research exposition (monographs, survey articles) pertaining to quantum theory
83E50	Supergravity
58A50	Supermanifolds and graded manifolds
14A22	Noncommutative algebraic geometry
32C11	Complex supergeometry

Keywords:

supergeometry; Radon-Penrose transform; Yang-Mills fields; twistor theory

Citations:

Zbl 0576.53002; Zbl 0641.53001