Global Variational Analysis (eBook)

Weierstrass Integrals on a Riemannian Manifold

Marston Morse (Autor)

eBook Download: PDF

2015
270 Seiten
Princeton University Press (Verlag)
978-1-4008-7043-1 (ISBN)

Infos

This book builds upon the revolutionary discovery made in 1974 that when one passes from function f to a function J of paths joining two points A1=A1 the connectivities R1 of the domain of f can be replaced by connectivities R1 over Q, common to the pathwise components of a basic Frechet space of classes of equivalent curves joining A1 to A1. The connectivities R1, termed "e;Frechet numbers,"e; are proved independent of the choice of A1 = A1, and of a replacement of Mn by any differential manifold homeomorphic to Mn.Originally published in 1976.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Produkt-Details

• Erscheint lt. Verlag: 8.3.2015
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Monographs in Population Biology
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Legacy Library
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: algebraic topology • analytic function • arc length • Axiom • Bernhard Riemann • Boundary value problem • Cartesian coordinate system • coefficient • Compact space • Computation • conjugate points • Connectivity (graph theory) • continuous function • corollary • Countable set • Counting • Cramer's Rule • Curve • deformation theory • Degeneracy (mathematics) • Derivative • diffeomorphism • differentiable manifold • differential equation • Differential Geometry • Differential structure • Dimension • Domain of a function • Eilenberg • Einstein notation • Equation • Euclidean space • Euler characteristic • Euler equations (fluid dynamics) • Euler integral • existence theorem • existential quantification • Exotic sphere • Family of curves • Finite set • First variation • Geometry • Global Analysis • Homeomorphism • Homology (mathematics) • Homotopy • implicit function theorem • inference • Integer • Intersection (set theory) • Interval (mathematics) • Invertible matrix • Jacobian matrix and determinant • Lagrange multiplier • Linear combination • Linear map • Line–line intersection • Mathematical Proof • Maximal set • Metric Space • Neighbourhood (mathematics) • N-sphere • Null vector • Open set • pairwise • Parameter • parametric equation • parametrization • partial derivative • Partial function • Phase space • Positive definiteness • projective plane • Quadratic • quadratic form • Rate of Convergence • Rational number • Real variable • resultant • Riemannian manifold • scientific notation • Sign (mathematics) • Special case • Sturm separation theorem • submanifold • subsequence • Subset • Taylor's theorem • Tensor Algebra • Theorem • theory • Topological Manifold • Topological space • Topology • Tuple • Unit vector • Variable (mathematics) • variational analysis • Weierstrass function • Without loss of generality
• ISBN-10: 1-4008-7043-7 / 1400870437
• ISBN-13: 978-1-4008-7043-1 / 9781400870431