About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 55. Chapters: Lipschitz continuity, Symplectic manifold, Riemannian manifold, Diffeology, Holonomy, Generalized complex structure, Fubini-Study metric, Spin structure, Calabi-Yau manifold, Almost complex manifold, Contact geometry, G-structure, CR manifold, Finsler manifold, Foliation, Nilmanifold, Triangulation, Supermanifold, Calibrated geometry, Hermitian manifold, Poisson manifold, Reduction of the structure group, Banach manifold, Pseudo-Riemannian manifold, Kahler manifold, Hyperkahler manifold, Hilbert manifold, Open book decomposition, Sasakian manifold, G2 manifold, Quaternion-Kahler manifold, Hauptvermutung, Hypercomplex manifold, Affine manifold, Quaternion-Kahler symmetric space, Solvmanifold, Piecewise linear manifold, Frechet manifold, Simplicial manifold, Parallelizable manifold, Hilbert-Smith conjecture, G2-structure, Kodaira embedding theorem, Symplectization, Spin(7)-manifold, Frolicher space, Pachner moves, Kirby-Siebenmann class, Schur's lemma, Hadamard manifold, Hermitian connection, Toric manifold, Almost symplectic manifold, Analytic manifold. Excerpt: In differential geometry, the holonomy of a connection on a smooth manifold is a general geometrical consequence of the curvature of the connection measuring the extent to which parallel transport around closed loops fails to preserve the geometrical data being transported. For flat connections, the associated holonomy is a type of monodromy, and is an inherently global notion. For curved connections, holonomy has nontrivial local and global features. Any kind of connection on a manifold gives rise, through its parallel transport maps, to some notion of holonomy. The most common forms of holonomy are for connections possessing some kind of symmetry. Important examples include: holonomy of the Levi-Civita connection in Riemannian geometry (called Riemannian ho...
