Foundations of Differential Geometry, Volume 2This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques. |
Contents
Submanifolds | 1 |
Covariant differentiation and second fundamental form | 10 |
Equations of Gauss and Codazzi | 26 |
Copyright | |
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Foundations of Differential Geometry, Volume 2 Shoshichi Kobayashi,Katsumi Nomizu Limited preview - 1996 |
Common terms and phrases
affine connection algebra g Amer automorphism canonical connection canonical decomposition Chapter Chern compact type complex manifold complex structure connection form coordinate system Corollary curvature form curvature tensor defined denote differentiable dimension element equation Euclidean space Example follows function G-structure g₁ GL(n Hence Hermitian holonomy group homogeneous space hypersurface imbedding implies induced inner product invariant irreducible isomorphism isotropy Jacobi field K-invariant Kaehler manifold Lemma Let G Lie group M₁ mapping Math metric g n-dimensional negative-definite neighborhood obtain orthogonal symmetric Lie orthonormal principal fibre bundle proof of Theorem Proposition prove resp respect restriction Ricci tensor Riemannian connection Riemannian manifold Riemannian metric sectional curvature semi-simple simply connected SO(n subalgebra subgroup subspace symmetric Lie algebra symmetric space tangent space tangent vector tensor field torsion variétés vector bundle vector fields vector space