文档介绍：GRAVITATION, GAUGE THEORIES AND
DIFFERENTIAL GEOMETRY
Tohru EGUCHI
Stanford Linear Accelerator Center, Stanford, California 94305, USA and The Enrico Fermi Institute and
Department of Physics, The University of Chicago, Chicago, illinois, USA
Peter B. GILKEY
Fine Hall, Box 37. Department of Mathematics, Princeton University, Princeton, New Jersey 08544, USA
and Department of Mathematics, University of Southern California, Los Angeles, California 90007, USA
and
Andrew J. HANSON
Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720, USA and
. Box 11693A, Palo Alto, California 94306, USA
I -
NORTH-HOLLAND PANY AMSTERDAM
PHYSICS REPORTS (Review Section of Physics Letters) 66. No. 6 (1980) 213—393. NORTH-HOLLAND PANY
GRAVITATION, GAUGE THEORIES AND DIFFERENTIAL GEOMETRY
Tohru EGUCHI*t
Stanford Linear Accierator Center. Stanford. California 94305. USA
and
The Enrico Fermi Institute and Department of Physics ft, The University of Chicago. Chicago. Illinois 60637. USA
Peter B. GILKEY**
Fine Hall, Box 37. Department of Mathematics, Princeton University. Princeton. New Jersey 08544, USA
and
Department of Mathematicstt, University of Southern California, Los Angeles. California 96(107. USA
and
Andrew J. HANSON*
Lawrence Berkeley Laboratory, University of California. Berkeley, California 94720, USA
and
. Box lJ693Att, Palo Alto, California 94306, USA
Received 19 March 1980
Contents
I. Introduction 215 3. Riemannian manifolds 241
. Gauge theories 216 . Cartan structure equations 241
. Gravitation 217 . Relation to classical tensor calculus 244
. Outline 218 . Einstein’s equations and self-dual manifolds 249
2. Manifolds and differential forms 219 . Complex manifolds 254
. Definition of a manifold 219 4. Geometry of fiber bundles 259
. Tangent space and cotangent space 222 . Fiber bundles 259
. Differential forms 224 . Vector bundles 263