By Shiing-Shen Chern, Wei-Huan Chen, K. S. Lam
This booklet is a translation of an authoritative introductory textual content according to a lecture sequence introduced through the popular differential geometer, Professor S S Chern in Beijing college in 1980. the unique chinese language textual content, authored via Professor Chern and Professor Wei-Huan Chen, used to be a special contribution to the math literature, combining simplicity and financial system of strategy with intensity of contents. the current translation is aimed toward a large viewers, together with (but no longer restricted to) complex undergraduate and graduate scholars in arithmetic, in addition to physicists drawn to the varied functions of differential geometry to physics. as well as a radical remedy of the basics of manifold idea, external algebra, the outside calculus, connections on fiber bundles, Riemannian geometry, Lie teams and relocating frames, and intricate manifolds (with a succinct advent to the speculation of Chern classes), and an appendix at the courting among differential geometry and theoretical physics, this e-book encompasses a new bankruptcy on Finsler geometry and a brand new appendix at the historical past and up to date advancements of differential geometry, the latter ready especially for this variation through Professor Chern to deliver the textual content into views.
By Saul Stahl
Tracing the formal improvement of Euclidean geometry, this article heavily follows Euclid's vintage, Elements. as well as offering a historic point of view on airplane geometry, it covers comparable themes, together with non-neutral Euclidean geometry, circles and standard polygons, projective geometry, symmetries, inversions, knots and hyperlinks, and casual topology. contains 1,000 perform difficulties. ideas on hand. 2003 version.
By C. Herbert Clemens, Michael A. Clemens (auth.)
Intended to be used in collage classes for potential or in-service secondary tuition lecturers of geometry. Designed to provide lecturers large training within the content material of ordinary geometry in addition to heavily comparable subject matters of a touch extra complex nature. The presentation and the modular structure are designed to include a versatile method for the instructing of geometry, one who could be tailored to varied lecture room settings. the fundamental technique is to boost the few primary techniques of trouble-free geometry, first in intuitive shape, after which extra carefully. the remainder of the cloth is then outfitted up out of those techniques via a mix of exposition and "guided discovery" within the challenge sections. A separate quantity together with the options to the workouts can be available.
By Christoph Hummel
Mikhail Gromov brought pseudo-holomorphic curves into symplectic geometry in 1985. on account that then, pseudo-holomorphic curves have taken on nice significance in lots of fields. the purpose of this booklet is to give the unique evidence of Gromov's compactness theorem for pseudo-holomorphic curves intimately. neighborhood houses of pseudo-holomorphic curves are investigated and proved from a geometrical point of view. homes of specific curiosity are isoperimetric inequalities, a monotonicity formulation, gradient bounds and the elimination of singularities. a different bankruptcy is dedicated to appropriate positive factors of hyperbolic surfaces, the place pairs of pants decomposition and thickthin decomposition are defined. The ebook is largely self-contained and may even be available to scholars with a uncomplicated wisdom of differentiable manifolds and protecting areas.
By Joseph O'Rourke, Jacob E. Goodman
Jacob E. Goodman, co-founder and editor of Discrete & Computational Geometry, the preeminent magazine in this quarter within the foreign arithmetic and desktop technological know-how group, joins forces with the celebrated machine scientist Joseph O'Rourke and different recognized experts to provide the definitive instruction manual on those interrelated fields.Over the previous decade or so, researchers and pros in discrete geometry and the more moderen box of computational geometry have built a hugely effective collaborative courting, the place each one region advantages from the equipment and insights of the opposite. whilst that discrete and computational geometry have gotten extra heavily pointed out, functions of the result of this paintings are getting used in progressively more generally differing components, from special effects and linear programming to production and robotics. The authors have spoke back the necessity for a entire handbookfor staff in those and comparable fields, and for different clients of the physique of results.While a lot details are available on discrete and computational geometry, it truly is scattered between many assets, and person books and articles are usually narrowly targeted. instruction manual of Discrete and Computational Geometry brings jointly, for the 1st time, the entire significant leads to either those fields into one quantity. hundreds of thousands of effects - theorems, algorithms, and tables - during the quantity definitively disguise the sphere, whereas a number of functions from many alternative fields exhibit sensible utilization. the cloth is gifted truly sufficient to aid the beginner, yet in adequate intensity to attract the expert. each technical time period is obviously outlined in an easy-to-use thesaurus. Over two hundred figures illustrate the innovations provided and supply assisting examples. details on present geometric software program - what it does, how successfully it does it, and the place to discover it - can also be incorporated.
By Ad Meskens, Paul Tytgat
By I. F. Sharygin
By Tim Bedford (auth.), Jacques Bélair, Serge Dubuc (eds.)
This ASI- which used to be additionally the twenty eighth consultation of the Seminaire de mathematiques superieures of the Universite de Montreal - used to be dedicated to Fractal Geometry and research. the current quantity is the fruit of the paintings of this complicated research Institute. We have been lucky to have with us Prof. Benoit Mandelbrot - the writer of diverse ideas in Fractal Geometry - who gave a sequence of lectures on multifractals, new release of analytic features, and diverse sorts of fractal stochastic procedures. varied foundational contributions for Fractal Geometry like degree conception, dy namical structures, generation conception, branching approaches are well-known. The geometry of fractal units and the analytical instruments used to enquire them offer a unifying topic of this publication. the most subject matters which are lined are then as follows. measurement conception. Many definitions of fractional size were proposed, all of which coincide on "regular" items, yet usually take various values for a given fractal set. there's plentiful dialogue on piecewise estimates yielding genuine values for the commonest dimensions (Hausdorff, box-counting and packing dimensions). The measurement thought is principally mentioned by way of Mendes-France, Bedford, Falconer, Tricot and Rata. building of fractal units. Scale in variance is a basic estate of fractal sets.
By Lee C. F. Sallows
This leading edge paintings by way of a British engineer initiates a Copernican revolution in our realizing of magic squares by means of exchanging numbers with two-dimensional types. the result's now not purely a unique type of geometrical magic sq. yet a revelation that conventional magic squares are actually greater noticeable because the one-dimensional example of this self-same geometrical activity.