Global Affine Differential Geometry of Hypersurfaces, An-Min Li, Udo Simon, Guosong Zhao, Zejun Hu

Автор: Ivan Cheltsov, Jihun Park
Название: Birationally Rigid Fano Threefold Hypersurfaces
ISBN: 1470423162 ISBN-13(EAN): 9781470423162
Издательство: Mare Nostrum (Eurospan)
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Цена: 74850.00 T
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Описание: The authors prove that every quasi-smooth weighted Fano threefold hypersurface in the 95 families of Fletcher and Reid is birationally rigid.

Автор: Thomas E. Cecil; Patrick J. Ryan
Название: Geometry of Hypersurfaces
ISBN: 1493945076 ISBN-13(EAN): 9781493945078
Издательство: Springer
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Цена: 102480.00 T
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Описание: This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms.

Автор: An-Min Li, Udo Simon, Guosong Zhao, Zejun Hu
Название: Global Affine Differential Geometry of Hypersurfaces
ISBN: 3110266679 ISBN-13(EAN): 9783110266672
Издательство: Walter de Gruyter
Цена: 148700.00 T
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Описание: This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry – as differential geometry in general – has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces.The second edition of this monograph leads the reader from introductory concepts to recent research. Since the publication of the first edition in 1993 there appeared important new contributions, like the solutions of two different affine Bernstein conjectures, due to Chern and Calabi, respectively. Moreover, a large subclass of hyperbolic affine spheres were classified in recent years, namely the locally strongly convex Blaschke hypersurfaces that have parallel cubic form with respect to the Levi-Civita connection of the Blaschke metric. The authors of this book present such results and new methods of proof.

Автор: Cecil Thomas E.
Название: Geometry of Hypersurfaces
ISBN: 1493932454 ISBN-13(EAN): 9781493932450
Издательство: Springer
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Цена: 111790.00 T
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Описание: This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms.

Автор: Claudio Dappiaggi; Valter Moretti; Nicola Pinamont
Название: Hadamard States from Light-like Hypersurfaces
ISBN: 3319643428 ISBN-13(EAN): 9783319643427
Издательство: Springer
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Цена: 51230.00 T
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Описание: This book provides a rather self-contained survey of the construction of Hadamard states for scalar field theories in a large class of notable spacetimes, possessing a (conformal) light-like boundary.

Автор: David Massey
Название: Le Cycles and Hypersurface Singularities
ISBN: 3540603956 ISBN-13(EAN): 9783540603955
Издательство: Springer
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Цена: 25110.00 T
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Описание: This text describes and gives applications of an important new tool in the study of complex analytic hypersurface singularities: the Le cycles of the hypersurface.

Автор: Eduardo Garcia-Rio, Peter Gilkey, Stana Nik?evi?, Ramon Vazquez-Lorenzo
Название: Applications of Affine and Weyl Geometry
ISBN: 1608457591 ISBN-13(EAN): 9781608457595
Издательство: Mare Nostrum (Eurospan)
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Цена: 46200.00 T
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Описание: Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannian extensions, and Kähler--Weyl geometry from this viewpoint. This book is intended to be accessible to mathematicians who are not expert in the subject and to students with a basic grounding in differential geometry. Consequently, the first chapter contains a comprehensive introduction to the basic results and definitions we shall need-proofs are included of many of these results to make it as self-contained as possible. Para-complex geometry plays an important role throughout the book and consequently is treated carefully in various chapters, as is the representation theory underlying various results. It is a feature of this book that, rather than as regarding para-complex geometry as an adjunct to complex geometry, instead, we shall often introduce the para-complex concepts first and only later pass to the complex setting.The second and third chapters are devoted to the study of various kinds of Riemannian extensions that associate to an affine structure on a manifold a corresponding metric of neutral signature on its cotangent bundle. These play a role in various questions involving the spectral geometry of the curvature operator and homogeneous connections on surfaces. The fourth chapter deals with Kähler--Weyl geometry, which lies, in a certain sense, midway between affine geometry and Kähler geometry. Another feature of the book is that we have tried wherever possible to find the original references in the subject for possible historical interest. Thus, we have cited the seminal papers of Levi-Civita, Ricci, Schouten, and Weyl, to name but a few exemplars. We have also given different proofs of various results than those that are given in the literature, to take advantage of the unified treatment of the area given herein.