By Johannes C C Nitsche
This 1989 monograph offers with parametric minimum surfaces in Euclidean area. the writer offers a huge survey which extends from the classical beginnings to the present state of affairs while highlighting a number of the subject's major beneficial properties and interspersing the mathematical improvement with pertinent historic comments. The presentation is whole and is complemented by means of a bibliography of approximately 1600 references. The cautious expository kind and emphasis on geometric elements are tremendous beneficial. furthermore, within the years best as much as the ebook of this e-book, the idea of minimum surfaces used to be discovering expanding program to different parts of arithmetic and the actual sciences making sure that this account will attract non-specialists to boot
By Manfredo P. Do Carmo
The booklet treats differential types and makes use of them to review a few neighborhood and international elements of the differential geometry of surfaces. Differential types are brought in an easy approach that would cause them to appealing to "users" of arithmetic. a short and hassle-free creation to differentiable manifolds is given in order that the most theorem, specifically the Stokes' theorem, could be provided in its ordinary environment. The functions consist in constructing the tactic of relocating frames of E. Cartan to review the neighborhood differential geometry of immersed surfaces in R3 in addition to the intrinsic geometry of surfaces. every thing is then prepare within the final bankruptcy to offer Chern's facts of the Gauss-Bonnet theorem for compact surfaces.
By Marco Abate, Francesca Tovena
L'opera fornisce una introduzione alla geometria delle variet� differenziabili, illustrandone le principali propriet� e descrivendo le principali tecniche e i più importanti strumenti usati according to il loro studio. Uno degli obiettivi primari dell'opera è di fungere da testo di riferimento in line with chi (matematici, fisici, ingegneri) united states l. a. geometria differenziale come strumento; inoltre può essere usato come libro di testo in step with diversi corsi introduttivi alla geometria differenziale, concentrandosi su alcuni dei vari aspetti della teoria presentati nell'opera. Più in dettaglio, nell'opera saranno trattati i seguenti argomenti: richiami di algebra multilineare e tensoriale, spesso non presentati nei corsi usual di algebra lineare; variet� differenziali, incluso il teorema di Whitney; fibrati vettoriali, incluso il teorema di Frobenius e un'introduzione ai fibrati principali; gruppi di Lie, incluso il teorema di corrispondenza fra sottogruppi e sottoalgebre; coomologia di de Rham, inclusa los angeles dualit� di Poincaré e il teorema di de Rham; connessioni, inclusa l. a. teoria delle geodetiche; e geometria Riemanniana, con particolare attenzione agli operatori di curvatura e inclusi teoremi di Cartan-Hadamard, Bonnet-Myers, e Synge-Weinstein. Come abitudine degli autori, il testo è scritto in modo da favorire una lettura attiva, cruciale in line with un buon apprendimento di argomenti matematici; inoltre è corredato da numerosi esempi svolti ed esercizi proposti.
By Theodore Frankel
This e-book offers a operating wisdom of these elements of external differential kinds, differential geometry, algebraic and differential topology, Lie teams, vector bundles, and Chern kinds which are invaluable for a deeper figuring out of either classical and smooth physics and engineering. it really is excellent for graduate and complicated undergraduate scholars of physics, engineering or arithmetic as a direction textual content or for self research.
a first-rate addition brought during this 3rd variation is the inclusion of an summary, which are learn ahead of beginning the textual content. This appears to be like first and foremost of the textual content, prior to bankruptcy 1. a number of the geometric recommendations built within the textual content are previewed right here and those are illustrated by means of their functions to a unmarried prolonged challenge in engineering, particularly the research of the Cauchy stresses created via a small twist of an elastic cylindrical rod approximately its axis
By Karl Friedrich Siburg
New variational tools by means of Aubry, Mather, and Mane, stumbled on within the final two decades, gave deep perception into the dynamics of convex Lagrangian structures. This publication exhibits how this precept of Least motion seems to be in various settings (billiards, size spectrum, Hofer geometry, glossy symplectic geometry). hence, subject matters from sleek dynamical structures and glossy symplectic geometry are associated in a brand new and infrequently mind-blowing method. The important item is Mather’s minimum motion practical. the extent is for graduate scholars onwards, but additionally for researchers in any of the themes touched within the book.
By Richard Courant
An exam of ways to easy-to-understand yet difficult-to-solve mathematical difficulties, this vintage textual content starts off with a dialogue of Dirichlet's precept and the boundary price challenge of capability conception, then proceeds to examinations of conformal mapping on parallel-slit domain names and Plateau's problem. Also explores minimum surfaces with unfastened barriers and risky minimum surfaces. 1950 version.
By Tobias H. Colding
By Lee J.M.
By Radu Miron (auth.)
From the reviews:
"The booklet is dedicated to an intensive examine of formal-geometric houses of higher-order nondegenerate one-dimensional variational integrals. … The author’s procedure turns out to be useful for the development of geometric types … . The booklet is exactly written, very transparent, in precept self-contained and will be understood by way of non-specialists." (Jan Chrastina, Zentralblatt MATH, Vol. 1044 (19), 2004)
By David Bachman
The smooth topic of differential types subsumes classical vector calculus. this article offers differential varieties from a geometrical viewpoint available on the complex undergraduate point. the writer ways the topic with the concept that complicated strategies could be equipped up via analogy from less complicated instances, which, being inherently geometric, usually could be most sensible understood visually.
Each new notion is gifted with a traditional photograph that scholars can simply clutch; algebraic homes then keep on with. This enables the improvement of differential types with out assuming a history in linear algebra. in the course of the textual content, emphasis is put on purposes in three dimensions, yet all definitions are given with a view to be simply generalized to raised dimensions.
The moment variation features a thoroughly new bankruptcy on differential geometry, in addition to different new sections, new routines and new examples. extra strategies to chose routines have additionally been incorporated. The paintings is appropriate to be used because the basic textbook for a sophomore-level category in vector calculus, in addition to for extra upper-level classes in differential topology and differential geometry.