Riemannian GeometryW. de Gruyter, 1982 - 396 páginas A section on foundations reviews differential calculus and topology and explains tensor bundles, Riemannian curvature, and isometric immersions, while subsequent sections on curvature and topology and structure of the geodesic flow present information on symmetric spaces, the sphere theorem, Hamiltonian systems, and the theorem of the three closed geodesics. This second edition includes material on the author's Main Theorem for Surfaces of Genus 0. Annotation copyright by Book News, Inc., Portland, OR |
Conteúdo
Foundations | 1 |
Curvature and Topology | 124 |
Structure of the Geodesic Flow | 256 |
Direitos autorais | |
1 outras seções não mostradas
Outras edições - Ver todos
Termos e frases comuns
1-parameter 2-plane a₁ a₂ Alexandrov triangle angle assume atlas bundle chart c(to c₁ canonical closed curves closed geodesic compact conjugate points consider constant curvature coordinates covariant derivation critical point D² E(c defined Definition denote diffeomorphism differentiable mapping E-value E₁ eigenvalue ellipsoid equation exists fibre finite flow line follows geodesic c(t geodesic flow given Hence Hilbert space homeomorphic homotopy hyperbolic isometry isomorphism Jacobi field K₁ Klingenberg Lemma length linear M₁ minimizing geodesic morphism orbit orthogonal P₁ Proof Proposition radius Remark Riemannian manifold Riemannian metric scalar product sectional curvature sequence simply connected sphere submanifold subset subspace sufficiently small symmetric space symplectic t₁ tangent bundle tangent space tensor Theorem totally geodesic u₁ u₂ V₁ vector bundle vector field x₁ Y₁