New edition of a successful Serge Lang titleWritten in the authors unique and engaging style, with clear and elegant proofsCovers the fundamentals of differential geometry, differential topology, and differential equationsIncludes new chapters on Jacobi lifts, tensorial splitting of the double tangent bundle, curvature and the variation formula, and an example of semi-negative curvatureNew chapters, sections, examples, and exercises have been added

Hersteller:
Springer Verlag GmbH
juergen.hartmann@springer.com
Tiergartenstr. 17
DE 69121 Heidelberg

I: GENERAL DIFFERENTIAL THEORY. 1: Differential Calculus. 2: Manifolds. 3: Vector Bundles. 4: Vector Fields and Differential Equations. 5: Operations on Vector Fields and Differential Forms. 6: The Theorem of Frobenius. II: METRICS, COVARIANT DERIVATIVES AND RIEMANNIAN GEOMETRY. 7: Metrics. 8: Covariant Derivatives and Geodesics. 9: Curvature. 10: Jacobi Lifts and Tensorial Splitting of the Double Tangent Bundle. 11: Curvature and the Variation Formula. 12: An Example of Seminegative Curvature. 13: Automorphisms and Symmetries. III: VOLUME FORMS AND INTEGRATION. 15: Volume Forms. 16: Integration of Differential Forms. 17: Stokes'' Theorem. 18: Applications of Stokes'' Theorem. Appendix: The Spectral Theorem.