DIFFERENTIAL AND PHYSICAL GEOMETRY
CONTENTS I PART I BACKGROUND APPETIZERS DI?ERENTIABLE MANIFOLDS THE TANGENT STRUCTURE LIE GROUPS I VECTOR BUNDLES LIE BRACKET AND LIE DERIVATIVE TENSORS AND DI?ERENTIAL FORMS INTEGRATION AND STOKES’ THEOREM 10 IMMERSION AND SUBMERSION 11 FIBER BUNDLES 12 LIE GROUPS II 13 DERHAM COHOMOLOGY 14 COMPLEX MANIFOLDS 15 LIE GROUPS AND LIE ALGEBRAS 16 LIE GROUP ACTIONS AND HOMOGENOUS SPACES 17 HOMOGENEOUS SPACES AND KLEIN GEOMETRIES 18 DISTRIBUTIONS AND FROBENIUS’ THEOREM 19 CONNECTIONS AND COVARIANT DERIVATIVES 20 RIEMANNIAN AND SEMI-RIEMANNIAN GEOMETRY 21 GEOMETRY OF SUBMANIFOLDS 23 COMPARISON THEOREMS 24 ALGEBRAIC TOPOLOGY 25 EHRESSMAN CONNECTIONS AND CARTAN CONNECTIONS II PART II 26 ANALYSIS ON MANIFOLDS 27 CLASSICAL MECHANICS 28 SYMPLECTIC GEOMETRY 29 POISSON GEOMETRY 30 QUANTIZATION 31 GENERAL RELATIVITY