Differential Geometry

By Martin Lipschutz

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By John P. D'Angelo

​​Hermitian research: From Fourier sequence to Cauchy-Riemann Geometry offers a coherent, built-in verify subject matters from undergraduate research. It starts off with Fourier sequence, keeps with Hilbert areas, discusses the Fourier remodel at the genuine line, after which turns to the center of the publication, geometric concerns. This bankruptcy contains advanced differential types, geometric inequalities from one and a number of other complicated variables, and comprises many of the author's effects. the idea that of orthogonality weaves the cloth right into a coherent complete. This textbook may be an invaluable source for upper-undergraduate scholars who intend to proceed with arithmetic, graduate scholars drawn to research, and researchers attracted to a few easy features of CR Geometry. The inclusion of a number of hundred workouts makes this e-book compatible for a capstone undergraduate Honors class.​

By Frédéric Cao

In picture processing, "motions by way of curvature" supply an effective method to delicate curves representing the bounds of items. In any such movement, every one aspect of the curve strikes, at any rapid, with a standard speed equivalent to a functionality of the curvature at this element. This ebook is a rigorous and self-contained exposition of the strategies of "motion by means of curvature". The method is axiomatic and formulated when it comes to geometric invariance with admire to the location of the observer. this is often translated into mathematical phrases, and the writer develops the technique of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then attracts a whole parallel with one other axiomatic technique utilizing level-set equipment: this results in generalized curvature motions. eventually, novel, and intensely exact, numerical schemes are proposed permitting one to compute the answer of hugely degenerate evolution equations in a totally invariant means. The convergence of this scheme can be proved.

By Jose G Vargas

This can be a ebook that the writer needs were to be had to him while he was once scholar. It displays his curiosity in figuring out (like specialist mathematicians) the main proper arithmetic for theoretical physics, yet within the kind of physicists. which means one isn't dealing with the examine of a set of definitions, comments, theorems, corollaries, lemmas, and so forth. yet a story the same as a narrative being instructed that doesn't bog down sophistication and deep effects.

It covers differential geometry a long way past what common relativists understand they should comprehend. And it introduces readers to different components of arithmetic which are of curiosity to physicists and mathematicians, yet are mostly neglected. between those is Clifford Algebra and its makes use of along side differential kinds and relocating frames. It opens new learn vistas that extend the subject material.

In an appendix at the classical idea of curves and surfaces, the writer slashes not just the most proofs of the normal technique, which makes use of vector calculus, yet even present remedies that still use differential varieties for a similar objective.

Readership: Physicists and mathematicians engaged on differential geometry.

By D. Ferus, W. Kühnel, U. Simon, B. Wegner

By V.I. Arnold, A.N. Varchenko, S.M. Gusein-Zade

V. 1. The type of serious issues, caustics and wave fronts -- v. 2. Monodromy and asymptotic of integrals

By Hanno Rund

The current monograph is prompted by way of precise goals. to start with, an endeavour has been made to provide a pretty entire account of the idea of Finsler areas in keeping with the equipment of classical differential geometry. Secondly, it truly is was hoping that this monograph may perhaps serve additionally as an advent to a department of differential geometry that is heavily relating to numerous themes in theoretical physics, particularly analytical dynamics and geometrical optics. With this moment item in brain, an test has been made to explain the elemental facets of the idea in a few element - even on the fee of conciseness - whereas within the extra specialized sections of the later chapters, that can be of curiosity mainly to the expert, a extra succinct variety has been followed. the truth that there exist numerous essentially various issues of view with reference to Finsler geometry has rendered the duty of writing a coherent account a slightly tough one. This comment is suitable not just to the advance of the topic at the foundation of the tensor calculus, yet is appropriate in a fair wider feel. The huge paintings of H. BUSEMANN has unfolded new avenues of method of Finsler geometry that are self sufficient of the tools of classical tensor research. within the latter experience, as a result, an entire description of this procedure doesn't fall in the scope of this treatise, even supposing its basic l value can't be doubted.

By Jacques Gasqui

This publication presents the 1st unified exam of the connection among Radon transforms on symmetric areas of compact kind and the infinitesimal models of 2 basic pressure difficulties in Riemannian geometry. Its fundamental concentration is the spectral stress challenge: Can the metric of a given Riemannian symmetric area of compact variety be characterised by way of the spectrum of its Laplacian? It additionally addresses a query rooted within the Blaschke challenge: Is a Riemannian metric on a projective house whose geodesics are all closed and of a similar size isometric to the canonical metric? The authors comprehensively deal with the consequences bearing on Radon transforms and the infinitesimal models of those difficulties. Their major end result means that so much Grassmannians are spectrally inflexible to the 1st order. this can be relatively vital, for there are nonetheless few isospectrality effects for certainly curved areas and those are the 1st such effects for symmetric areas of compact kind of rank >1. The authors make the most the idea of overdetermined partial differential equations and harmonic research on symmetric areas to supply standards for infinitesimal pressure that follow to a wide classification of areas. quite a lot of easy fabric approximately Riemannian geometry, symmetric areas, and Radon transforms is integrated in a transparent and chic presentation that may be worthwhile to researchers and complex scholars in differential geometry.

By Vladislav V Goldberg, Shiing-Shen Chern

Elie Cartan's e-book "Geometry of Riemannian Manifolds" (1928) was once the best introductions to his equipment. It used to be in line with lectures given by means of the writer on the Sorbonne within the educational 12 months 1925-26. A modernized and commonly augmented variation seemed in 1946 (2nd printing, 1951; third printing, 1988). Cartan's lectures in 1926-27 have been diversified - he brought external varieties on the very starting and used orthogonal frames all through to enquire the geometry of Riemannian manifolds. during this path, he solved a chain of difficulties in Euclidean and non-Euclidean areas, in addition to a chain of variational difficulties on geodesics. The lectures have been translated into Russian within the ebook "Riemannian Geometry in an Orthogonal body" (1960). This booklet has many inventions, resembling the inspiration of intrinsic basic differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional area or in an area of continuing curvature, an affine connection outlined in a regular fibre package of a submanifold, and so forth. This e-book was once to be had neither in English nor in French. It has now been translated into English through Vladislav V. Goldberg, presently uncommon Professor of arithmetic on the New Jersey Institute of expertise, united states, who edited the Russian version.

By Igor Dolgachev

This advent to the most principles of algebraic and geometric invariant idea assumes just a minimum heritage in algebraic geometry, algebra and illustration thought. subject matters lined comprise the symbolic technique for computation of invariants at the house of homogeneous types, the matter of finite-generatedness of the algebra of invariants, and the speculation of covariants and structures of express and geometric quotients. all through, the emphasis is on concrete examples that originate in classical algebraic geometry. Written in an available sort with many examples and routines, the publication deals a singular dialogue of attainable linearizations of activities and the difference of quotients below the switch of linearization.