"nonmetrisable Manifolds"

Differential Analysis on Complex Manifolds  eBooks & eLearning

Posted by AvaxGenius at Dec. 27, 2022
Differential Analysis on Complex Manifolds

Differential Analysis on Complex Manifolds by R. O. Wells
English | PDF | 1980 | 269 Pages | ISBN : N/A | 20.8 MB

In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems.

Differential Analysis on Complex Manifolds  eBooks & eLearning

Posted by AvaxGenius at Jan. 27, 2023
Differential Analysis on Complex Manifolds

Differential Analysis on Complex Manifolds by Raymond O. Wells
English | PDF | 2008 | 315 Pages | ISBN : 0387738916 | 1.9 MB

In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge *-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems.

Smooth Manifolds and Observables  eBooks & eLearning

Posted by AvaxGenius at Sept. 18, 2020
Smooth Manifolds and Observables

Smooth Manifolds and Observables by Jet Nestruev
English | EPUB | 2020 | 441 Pages | ISBN : 3030456498 | 39.25 MB

This textbook demonstrates how differential calculus, smooth manifolds, and commutative algebra constitute a unified whole, despite having arisen at different times and under different circumstances. Motivating this synthesis is the mathematical formalization of the process of observation from classical physics. A broad audience will appreciate this unique approach for the insight it gives into the underlying connections between geometry, physics, and commutative algebra.

Topology of Infinite-Dimensional Manifolds  eBooks & eLearning

Posted by AvaxGenius at Nov. 21, 2020
Topology of Infinite-Dimensional Manifolds

Topology of Infinite-Dimensional Manifolds by Katsuro Sakai
English | EPUB | 2020 | 631 Pages | ISBN : 9811575746 | 49.3 MB

An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the following spaces are considered model spaces: Hilbert space (or non-separable Hilbert spaces), the Hilbert cube, dense subspaces of Hilbert spaces being universal spaces for absolute Borel spaces, the direct limit of Euclidean spaces, and the direct limit of Hilbert cubes (which is homeomorphic to the dual of a separable infinite-dimensional Banach space with bounded weak-star topology).

Topology of Infinite-Dimensional Manifolds  eBooks & eLearning

Posted by roxul at Nov. 21, 2020
Topology of Infinite-Dimensional Manifolds

Katsuro Sakai, "Topology of Infinite-Dimensional Manifolds "
English | ISBN: 9811575746 | 2020 | 634 pages | PDF | 14 MB

Riemannian Manifolds and Homogeneous Geodesics  eBooks & eLearning

Posted by roxul at Nov. 6, 2020
Riemannian Manifolds and Homogeneous Geodesics

Valerii Berestovskii, "Riemannian Manifolds and Homogeneous Geodesics"
English | ISBN: 3030566579 | 2020 | 504 pages | PDF | 6 MB

Stochastic Calculus in Manifolds  eBooks & eLearning

Posted by AvaxGenius at July 8, 2022
Stochastic Calculus in Manifolds

Stochastic Calculus in Manifolds by Michel Emery
English | PDF | 1989 | 158 Pages | ISBN : 3540516646 | 18 MB

Addressed to both pure and applied probabilitists, including graduate students, this text is a pedagogically-oriented introduction to the Schwartz-Meyer second-order geometry and its use in stochastic calculus. P.A. Meyer has contributed an appendix: "A short presentation of stochastic calculus" presenting the basis of stochastic calculus and thus making the book better accessible to non-probabilitists also. No prior knowledge of differential geometry is assumed of the reader: this is covered within the text to the extent.

Introduction to Smooth Manifolds  eBooks & eLearning

Posted by AvaxGenius at Jan. 31, 2025
Introduction to Smooth Manifolds

Introduction to Smooth Manifolds by John M. Lee
English | PDF (True) | 2012 | 723 Pages | ISBN : 1441999817 | 7.4 MB

This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research–- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer.

Manifolds, Tensor Analysis, and Applications  eBooks & eLearning

Posted by AvaxGenius at Nov. 20, 2022
Manifolds, Tensor Analysis, and Applications

Manifolds, Tensor Analysis, and Applications by Ralph Abraham, Jerrold E. Marsden, Tudor Ratiu
English | PDF | 1988 | 666 Pages | ISBN : 0387967907 | 43.5 MB

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me­ chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory.

Foundations of Hyperbolic Manifolds  eBooks & eLearning

Posted by AvaxGenius at Feb. 15, 2025
Foundations of Hyperbolic Manifolds

Foundations of Hyperbolic Manifolds by John G. Ratcliffe
English | PDF (True) | 2006 | 794 Pages | ISBN : 0387331972 | 5.4 MB

This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference.