Einstein Manifolds

Einstein Manifolds PDF

Author: Arthur L. Besse

Publisher: Springer Science & Business Media

Published: 2007-12-03

Total Pages: 529

ISBN-13: 3540741208

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Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. This is the first book which presents an overview of several striking results ensuing from the examination of Einstein’s equations in the context of Riemannian manifolds. Parts of the text can be used as an introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.

Essays on Einstein Manifolds

Essays on Einstein Manifolds PDF

Author: Claude LeBrun

Publisher: American Mathematical Society(RI)

Published: 1999

Total Pages: 450

ISBN-13:

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This is the sixth volume in a series providing surveys of differential geometry. It addresses: Einstein manifolds with zero Ricci curvature; rigidity and compactness of Einstein metrics; general relativity; the stability of Minkowski space-time; and more.

Riemannian Topology and Geometric Structures on Manifolds

Riemannian Topology and Geometric Structures on Manifolds PDF

Author: Krzysztof Galicki

Publisher: Springer Science & Business Media

Published: 2010-07-25

Total Pages: 303

ISBN-13: 0817647430

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Riemannian Topology and Structures on Manifolds results from a similarly entitled conference held on the occasion of Charles P. Boyer’s 65th birthday. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory. Focusing on these fundamental ideas, this collection presents review articles, original results, and open problems of interest.

International Journal of Mathematical Combinatorics, Volume 3, 2018

International Journal of Mathematical Combinatorics, Volume 3, 2018 PDF

Author: Linfan Mao

Publisher: Infinite Study

Published:

Total Pages: 165

ISBN-13:

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The International J. Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.

Null Curves and Hypersurfaces of Semi-Riemannian Manifolds

Null Curves and Hypersurfaces of Semi-Riemannian Manifolds PDF

Author: Krishan L. Duggal

Publisher: World Scientific

Published: 2007

Total Pages: 302

ISBN-13: 981270647X

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This is a first textbook that is entirely focused on the up-to-date developments of null curves with their applications to science and engineering. It fills an important gap in a second-level course in differential geometry, as well as being essential for a core undergraduate course on Riemannian curves and surfaces. The sequence of chapters is arranged to provide in-depth understanding of a chapter and stimulate further interest in the next. The book comprises a large variety of solved examples and rigorous exercises that range from elementary to higher levels. This unique volume is self-contained and unified in presenting: ? A systematic account of all possible null curves, their Frenet equations, unique null Cartan curves in Lorentzian manifolds and their practical problems in science and engineering.? The geometric and physical significance of null geodesics, mechanical systems involving curvature of null curves, simple variation problems and the interrelation of null curves with hypersurfaces.

Kähler Immersions of Kähler Manifolds into Complex Space Forms

Kähler Immersions of Kähler Manifolds into Complex Space Forms PDF

Author: Andrea Loi

Publisher: Springer

Published: 2018-09-20

Total Pages: 100

ISBN-13: 3319994832

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The aim of this book is to describe Calabi's original work on Kähler immersions of Kähler manifolds into complex space forms, to provide a detailed account of what is known today on the subject and to point out some open problems. Calabi's pioneering work, making use of the powerful tool of the diastasis function, allowed him to obtain necessary and sufficient conditions for a neighbourhood of a point to be locally Kähler immersed into a finite or infinite-dimensional complex space form. This led to a classification of (finite-dimensional) complex space forms admitting a Kähler immersion into another, and to decades of further research on the subject. Each chapter begins with a brief summary of the topics to be discussed and ends with a list of exercises designed to test the reader's understanding. Apart from the section on Kähler immersions of homogeneous bounded domains into the infinite complex projective space, which could be skipped without compromising the understanding of the rest of the book, the prerequisites to read this book are a basic knowledge of complex and Kähler geometry.

Complex, Contact and Symmetric Manifolds

Complex, Contact and Symmetric Manifolds PDF

Author: Oldrich Kowalski

Publisher: Springer Science & Business Media

Published: 2007-07-28

Total Pages: 277

ISBN-13: 0817644245

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* Contains research and survey articles by well known and respected mathematicians on recent developments and research trends in differential geometry and topology * Dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields * Papers include all necessary introductory and contextual material to appeal to non-specialists, as well as researchers and differential geometers

Osserman Manifolds in Semi-Riemannian Geometry

Osserman Manifolds in Semi-Riemannian Geometry PDF

Author: Eduardo Garcia-Rio

Publisher: Springer

Published: 2004-10-14

Total Pages: 170

ISBN-13: 3540456295

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The subject of this book is Osserman semi-Riemannian manifolds, and in particular, the Osserman conjecture in semi-Riemannian geometry. The treatment is pitched at the intermediate graduate level and requires some intermediate knowledge of differential geometry. The notation is mostly coordinate-free and the terminology is that of modern differential geometry. Known results toward the complete proof of Riemannian Osserman conjecture are given and the Osserman conjecture in Lorentzian geometry is proved completely. Counterexamples to the Osserman conjuncture in generic semi-Riemannian signature are provided and properties of semi-Riemannian Osserman manifolds are investigated.

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