TOPICS IN DIFFERENTIAL GEOMETRY

By BARBARA JONES

CHAPTER I MANIFOLDS AND VECTOR FIELDS 1 DI?ERENTIABLE MANIFOLDS 2 SUBMERSIONS AND IMMERSIONS C COVERING SPACES AND FUNDAMENTAL GROUPS 3 VECTOR FIELDS AND FLOWS CHAPTER II LIE GROUPS 4 LIE GROUPS I 5 LIE GROUPS II LIE SUBGROUPS AND HOMOGENEOUS SPACES CHAPTER III DI?ERENTIAL FORMS AND DE RHAM COHOMOLOGY 6 VECTOR BUNDLES 7 DI?ERENTIAL FORMS 8 INTEGRATION ON MANIFOLDS 9 DE RHAM COHOMOLOGY 10 COHOMOLOGY WITH COMPACT SUPPORTS AND POINCAR´E DUALITY 11 DE RHAM COHOMOLOGY OF COMPACT MANIFOLDS 12 LIE GROUPS III ANALYSIS ON LIE GROUPS CHAPTER IV RIEMANNIAN GEOMETRY 13 PSEUDO RIEMANN METRICS AND THE LEVI CIVITA COVARIANT DERIVATIVE 14 RIEMANN GEOMETRY OF GEODESICS 15 PARALLEL TRANSPORT AND CURVATURE 16 COMPUTING WITH ADAPTED FRAMES, AND EXAMPLES 17 RIEMANN IMMERSIONS AND SUBMERSIONS 18 JACOBI ?ELDS H HODGE THEORY CHAPTER V BUNDLES AND CONNECTIONS 19 DERIVATIONS ON THE ALGEBRA OF DI?ERENTIAL FORMS AND THE FR¨OLICHER-NIJENHUIS BRACKET 20 FIBER BUNDLES AND CONNECTIONS 21 PRINCIPAL FIBER BUNDLES AND G-BUNDLES 22 PRINCIPAL AND INDUCED CONNECTIONS 23 CHARACTERISTIC CLASSES 24 JETS CHAPTER VI SYMPLECTIC GEOMETRY AND HAMILTONIAN MECHANICS 25 SYMPLECTIC GEOMETRY AND CLASSICAL MECHANICS 26 COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS 27 EXTENSIONS OF LIE ALGEBRAS AND LIE GROUPS 28 POISSON MANIFOLDS 29 HAMILTONIAN GROUP ACTIONS AND MOMENTUM MAPPINGS 30 LIE POISSON GROUPS REFERENCES