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Lie Sphere Geometry: With Applications to Submanifolds
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Thomas E Cecil
This book provides a clear and comprehensive modern treatment of Lie sphere geometry and its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. The link with Euclidean ...
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Hyperfunctions on Hypo-Analytic Manifolds
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Paulo D Cordaro, Paulo D Coraro, Francois Treves
In the first two chapters of this book, the reader will find a complete and systematic exposition of the theory of hyperfunctions on totally real submanifolds of multidimensional complex space, in particular of hyperfunction theory in real space. The book provides precise definitions of the hypoanalytic wave-front set and of the Fourier-Bros ...
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Spherical Cr Geometry and Dehn Surgery
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by
Richard Evan Schwartz
This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds which bound complex hyperbolic orbifolds - the only known ...
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Differential Geometry and Analysis on Cr Manifolds
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by
Sorin Dragomir, Giuseppe Tomassini
The study of CR manifolds lies at the intersection of three main mathematical disciplines: partial differential equations, complex analysis in several complex variables, and differential geometry. While the PDE and complex analytic aspects have been intensely studied in the last fifty years, much effort has recently been made to understand the ...
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Submanifolds and Holonomy
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Jurgen Berndt, Sergio Console, Carlos Olmos
With special emphasis on new techniques based on the holonomy of the normal connection, this book provides an up-to-date, complete introduction to submanifold geometry. It offers a thorough survey of these techniques and their applications and presents a framework for various recent results to date found only in scattered research papers. The ...
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Generalized Cauchy-Riemann Systems with a Singular Point
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by
Usmanov
A theory of generalized Cauchy-Riemann systems with polar singularities of order not less than one is presented and its application to study of infinitesimal bending of surfaces having positive curvature and an isolated flat point is given. The book contains results of investigations obtained by the author and his collaborators.
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An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem
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Luca Capogna, Donatella Danielli, Scott D Pauls
This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile. It presents a detailed description of Heisenberg ...
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Cr Manifolds and the Tangential Cauchy-Riemann Complex
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by
Boggess
"CR Manifolds and the Tangential Cauchy Riemann Complex" provides an elementary introduction to CR manifolds and the tangential Cauchy-Riemann Complex and presents some of the most important recent developments in the field. The first half of the book covers the basic definitions and background material concerning CR manifolds, CR functions, the ...
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Higher Order Contact of Submanifolds of Homogeneous Spaces
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by
G R Jensen
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Real Submanifolds in Complex Space and Their Mappings (PMS-47)
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by
M Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild
This book presents many of the main developments of the past two decades in the study of real submanifolds in complex space, providing crucial background material for researchers and advanced graduate students. The techniques in this area borrow from real and complex analysis and partial differential equations, as well as from differential, ...
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Tight and Taut Submanifolds
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by
Thomas E. Cecil (Editor), Shiing-Shen Chern (Editor)
Tight and taut manifolds form an important and special class of surfaces within differential geometry. This book contains in-depth articles by experts in the field as well as an extensive and comprehensive bibliography. This survey will open new avenues for further research and will be an important addition to any geometer's library.
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Complex Analysis and Cr Geometry
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by
G Zampieri
Cauchy-Riemann (CR) geometry is the study of manifolds equipped with a system of CR-type equations. Compared to the early days when the purpose of CR geometry was to supply tools for the analysis of the existence and regularity of solutions to the $\bar\partial$-Neumann problem, it has rapidly acquired a life of its own and has became an important ...
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Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications
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by
Krishan L Duggal, A Bejancu, Jonathon Liebenau (Editor)
This book has been written with a two-fold approach in mind: firstly, it adds to the theory of submanifolds the missing part of lightlike (degenerate) submanifolds of semi-Riemannian manifolds, and, secondly, it applies relevant mathematical results to branches of physics. It is the first-ever attempt in mathematical literature to present the most ...
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Critical point theory and submanifold geometry
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by
Richard S Palais
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Projective Differential Geometry of Submanifolds
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by
Akivis, Golberg
In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis ...
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Sub-Riemannian Geometry: General Theory and Examples
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by
Ovidiu Calin, Der-Chen Chang
Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples ...
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Geometry of Pseudo-Finsler Submanifolds
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by
Aurel Bejancu, Hani Reda Farran
This book begins with a new approach to the geometry of pseudo-Finsler manifolds. It also discusses the geometry of pseudo-Finsler manifolds and presents a comparison between the induced and the intrinsic Finsler connections. The Cartan, Berwald, and Rund connections are all investigated. Included also is the study of totally geodesic and other ...
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Curves and Surfaces
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by
Sebastian Montiel
This introductory textbook puts forth a clear and focused point of view on the differential geometry of curves and surfaces. Following the modern point of view on differential geometry, the book emphasizes the global aspects of the subject. The excellent collection of examples and exercises (with hints) will help students in learning the material. ...
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Singularities and Complex Geometry: Seminar on Singularities and Complex Geometry, June 15-20, 1994, Beijing, China
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by
Qikeng Lu
This book represents the proceedings of the joint U.S.-China Seminar on Singularity and Complex Geometry held at the Institute of Mathematics of the Chinese Academy, Beijing, in June 1994. This was the first gathering of Chinese and American mathematicians working in these fields (several Japanese mathematicians also took part). The volume covers ...
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Seminar on Minimal Submanifolds
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by
Enrico Bombieri
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Invariant Manifolds
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by
Morris W Hirsch
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Geometry and Topology of Submanifolds IX
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by
F Defever (Editor), L Verstraelen (Editor), G Zafindratafa (Editor)
This text covers topics such as: contract metric R-harmonic manifolds; hypersurfaces in space forms with some constant curvature functions; manifolds of pseudodynamics; cubic forms generated by functions on projectively flat spaces; and distinguished submanifolds of a Sasakian manifold.
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The Submanifold Geometries Associated to Grassmannian Systems
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by
Martina Bruck
This work is intended for graduate students and research mathematicians interested in differential geometry and partial differential equations.
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An Introduction to Cr Structures
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by
Howard Jacobowitz
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Differential geometry of submanifolds proceedings of the conference held at Kyoto, January 23-25, 1984
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by
Kenmotsu
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