Global Riemannian Geometry: Curvature and Topology, Hurtado Ana, Markvorsen Steen, Min-Oo Maung

Автор: John Douglas Moore
Название: Introduction to Global Analysis: Minimal Surfaces in Riemannian Manifolds
ISBN: 1470429500 ISBN-13(EAN): 9781470429508
Издательство: Mare Nostrum (Eurospan)
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Цена: 112860.00 T
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Описание: During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold $M$ determine the homology of the manifold.Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on $M$ by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs.This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed parametrized minimal surfaces in a compact Riemannian manifold, establishing Morse inequalities for perturbed versions of the energy function on the mapping space. It studies the bubbling which occurs when the perturbation is turned off, together with applications to the existence of closed minimal surfaces. The Morse-Sard theorem is used to develop transversality theory for both closed geodesics and closed minimal surfaces.This book is based on lecture notes for graduate courses on "Topics in Differential Geometry", taught by the author over several years. The reader is assumed to have taken basic graduate courses in differential geometry and algebraic topology.

Автор: Javier de Lucas, Cristina Sardon Munoz
Название: A Guide to Lie Systems with Compatible Geometric Structures
ISBN: 1786346974 ISBN-13(EAN): 9781786346971
Издательство: World Scientific Publishing
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Цена: 142560.00 T
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The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.

Offering a complete overview from the topic's foundations to the present, this book is an ideal resource for Physics and Mathematics students, doctoral students and researchers.

Автор: Lyndon Woodward, John Bolton
Название: A First Course in Differential Geometry: Surfaces in Euclidean Space
ISBN: 1108424937 ISBN-13(EAN): 9781108424936
Издательство: Cambridge Academ
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Цена: 80250.00 T
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Описание: This textbook covers the classical topics of differential geometry of surfaces as studied by Gauss: the definition and geometric meaning of Gaussian curvature, the Theorema Egregium, geodesics, and the Gauss-Bonnet Theorem. It is suitable for upper-level undergraduates and contains plentiful examples and exercises, with solutions to selected problems.

Автор: Izumiya Shyuichi, Fuster Maria Del Carmen Romero, Ruas Maria Aparecida Soares
Название: Differential Geometry from Singularity Theory Viewpoint
ISBN: 9814590444 ISBN-13(EAN): 9789814590440
Издательство: World Scientific Publishing
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Цена: 126720.00 T
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Описание: 'The present book has been enriched by including, in the Notes of each chapter, other aspects and studies on the topics in questions and by providing a wide list of references. The book will be a helpful tool for researchers interested in the field and in particular, in the study of the differential geometry of singular submanifolds of Euclidean and Minkowski spaces.'European Mathematical SocietyDifferential Geometry from a Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wavefronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces.

Название: Moduli Spaces Of Real Projective Structures On Surfaces
ISBN: 4864970963 ISBN-13(EAN): 9784864970969
Издательство: World Scientific Publishing
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Цена: 21120.00 T
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Описание: This book is an excellent first encounter with the burgeoning field of real projective manifolds. It gives a comprehensive introduction to the theory of real projective structures on surfaces and their moduli spaces. A central theme is an attractive parameterisation of moduli space discovered by Fock and Goncharov that allows the explicit description or analysis of many key features. These include a natural Poisson structure, the effect of projective duality, holonomy representations and the geometry of ends, to name but a few.This book is written with two kinds of readers in mind: those who would like to learn about real projective surfaces or manifolds, and those who have a passing knowledge thereof but are interested in the geometric underpinnings of Fock and Goncharov's parameterisation of moduli space of certain real projective structures.The material is accessible to any mathematician interested in these topics. It is presented in a self-contained manner with minimal prerequisites. Applications of Fock and Goncharov's parameterisation of moduli space presented in this book include new proofs of results by Teichmuller (1939) concerning hyperbolic structures, by Goldman (1990) concerning closed surfaces, and by Marquis (2010) concerning structures of finite area.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

Автор: Simon Donaldson
Название: Selected Papers from the Journal of Differential Geometry 1967-2017, Volume 4
ISBN: 1571463372 ISBN-13(EAN): 9781571463371
Издательство: Mare Nostrum (Eurospan)
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Цена: 39730.00 T
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Описание: Presents twelve important papers which have formed some the cornerstones of geometric analysis. Their subject matter ranges over the areas of conformal geometry, gauge theory, symplectic geometry, mean curvature, spectral theory, and general relativity.

Автор: Yekutieli Amnon
Название: Nonabelian Multiplicative Integration On Surfaces
ISBN: 9814663840 ISBN-13(EAN): 9789814663847
Издательство: World Scientific Publishing
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Цена: 61250.00 T
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Описание: Nonabelian multiplicative integration on curves is a classical theory. This volume is about the 2-dimensional case, which is much more difficult.

Автор: Dundas Bjшrn Ian
Название: Short Course in Differential Topology
ISBN: 1108425798 ISBN-13(EAN): 9781108425797
Издательство: Cambridge Academ
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Цена: 49630.00 T
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Описание: This book offers a concise and modern introduction to differential topology, the study of smooth manifolds and their properties, at the advanced undergraduate/beginning graduate level. The treatment throughout is hands-on, including many concrete examples and exercises woven into the text with hints provided to guide the student.

Автор: Geiges
Название: The Geometry of Celestial Mechanics
ISBN: 1107564808 ISBN-13(EAN): 9781107564800
Издательство: Cambridge Academ
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Цена: 40130.00 T
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Описание: A geometric introduction to celestial mechanics, for advanced undergraduate and beginning graduate students. This textbook introduces the geometric concepts underlying celestial mechanics and their applications, making it suitable for traditional geometry courses or as supplementary material. Numerous exercises and extensive historical notes also support self-study.

Автор: Simon Donaldson
Название: Selected Papers from the Journal of Differential Geometry 1967-2017, Volume 5
ISBN: 1571463380 ISBN-13(EAN): 9781571463388
Издательство: Mare Nostrum (Eurospan)
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Цена: 39730.00 T
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Описание: Presents eleven papers dealing with geometric PDEs, geometric flows, and related subject areas. Among the authors and topics are: Richard S. Hamilton on three-manifolds with positive Ricci curvature; Gerhard Huisken on flow by mean curvature of convex surfaces into spheres; and L.C. Evans and J. Spruck on motion of level sets by mean curvature.

Автор: Woodward Lyndon
Название: First Course in Differential Geometry
ISBN: 1108441025 ISBN-13(EAN): 9781108441025
Издательство: Cambridge Academ
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Цена: 38010.00 T
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Описание: This textbook covers the classical topics of differential geometry of surfaces as studied by Gauss: the definition and geometric meaning of Gaussian curvature, the Theorema Egregium, geodesics, and the Gauss-Bonnet Theorem. It is suitable for upper-level undergraduates and contains plentiful examples and exercises, with solutions to selected problems.

Автор: Guillemin Victor, Haine Peter
Название: Differential Forms
ISBN: 9811213771 ISBN-13(EAN): 9789811213779
Издательство: World Scientific Publishing
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Цена: 47520.00 T
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There already exist a number of excellent graduate textbooks on the theory of differential forms as well as a handful of very good undergraduate textbooks on multivariable calculus in which this subject is briefly touched upon but not elaborated on enough.

The goal of this textbook is to be readable and usable for undergraduates. It is entirely devoted to the subject of differential forms and explores a lot of its important ramifications.

In particular, our book provides a detailed and lucid account of a fundamental result in the theory of differential forms which is, as a rule, not touched upon in undergraduate texts: the isomorphism between the Čech cohomology groups of a differential manifold and its de Rham cohomology groups.