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Tight and Taut Submanifolds
First published in 1997, this book contains six in-depth articles on various aspects of the field of tight and taut submanifolds and concludes with an extensive bibliography of the entire field. The book is dedicated to the memory of Nicolaas H. Kuiper; the first paper is an unfinished but insightful survey of the field of tight immersions and maps written by Kuiper himself. Other papers by leading researchers in the field treat topics such as the smooth and polyhedral portions of the theory of tight immersions, taut, Dupin and isoparametric submanifolds of Euclidean space, taut submanifolds of arbitrary complete Riemannian manifolds, and real hypersurfaces in complex space forms with special curvature properties. Taken together these articles provide a comprehensive survey of the field and point toward several directions for future research.
Recent Developments in Pseudo-Riemannian Geometry
This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are: Classification of pseudo-Riemannian symmetric spaces Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential conformal structures and conformal transformations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian manifolds Lorentzian symme...
Conformal Differential Geometry
Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. The aim of the seminar was to present the basic ideas and some of the recent developments around Q-curvature and conformal holonomy. The part on Q-curvature discusses its origin, its relevance in geometry, spectral theory and physics. Here the influence of ideas which have their origin in the AdS/CFT-correspondence becomes visible. The part on conformal holonomy describes recent classification results, its relation to Einstein metrics and to conformal Killing spinors, and related special geometries.
Blowups, Slicings and Permutation Groups in Combinatorial Topology
Combinatorial topology is a field of research that lies in the intersection of geometric topology, combinatorics, algebraic topology and polytope theory. The main objects of interest are piecewise linear topological manifolds where the manifold is given as a simplicial complex with some additional combinatorial structure. These objects are called combinatorial manifolds. In this work, elements and concepts of algebraic geometry, such as blowups, Morse theory as well as group theory are translated into the field of combinatorial topology in order to establish new tools to study combinatorial manifolds. These tools are applied to triangulated surfaces, 3- and 4-manifolds with and without the help of a computer. Among other things, a new combinatorial triangulation of the K3 surface, combinatorial properties of normal surfaces, and new combinatorial triangulations of pseudomanifolds with multiply transitive automorphism group are presented.
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Dirac Operators in Riemannian Geometry
For a Riemannian manifold M, the geometry, topology and analysis are interrelated in ways that have become widely explored in modern mathematics. Bounds on the curvature can have significant implications for the topology of the manifold. The eigenvalues of the Laplacian are naturally linked to the geometry of the manifold. For manifolds that admit spin structures, one obtains further information from equations involving Dirac operators and spinor fields. In the case of four-manifolds, for example, one has the remarkable Seiberg-Witten invariants. In this text, Friedrich examines the Dirac operator on Riemannian manifolds, especially its connection with the underlying geometry and topology of...
Implantation of the Ovum
This book brings together authoritative accounts by leaders in the field of reproductive biology, researchers who have closely investigated implantation. The subject is approached from several angles: biochemical, endocrinological, pharmacological, anatomic, and immunological.
Rhinology and Facial Plastic Surgery
Georg von Bekesey was awarded the Nobel Prize for his seminal everyone all over the world. In other words it is directed toward work on hearing. It was, however, 43 years later in 2004 that evolving a common scientifc language that is spoken uniformly Linda Buck and Richard Axel were awarded the Nobel Prize for and consistently all over the world. Universality, so that norms, their work on olfaction. Tis is indicative of how the science of staging systems, etc., can be applied anywhere in the world with rhinology is only now coming into its own. For quite some time, equal validity. Tis can only be achieved through consensus. rhinology was thought to be limited in scope. It is now appreci- Tis book contains not only the genesis and pathogenesis of ated that the nose is not only an organ of aesthetic appeal, but rhinologic disease, but also what all surgeons want and that is one that carries out several important, complex functions. Te operative steps to bring about successful resolution of disease, tremendous surge in medical literature in recent times bears with the return of normal function.
Geometry of Hypersurfaces
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. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypers...
Neurogastroenterology - From the Basics to the Clinics
In the last decade, some outstanding progress has been made in the field of neurogastroenterology, a term which has been introduced to account for the crucial role of the enteric, autonomic and central nervous system in the regulation of gastrointestinal functions in health and disease. These proceedings of Falk Symposium No. 112 on Neurogastroenterology - From the Basics to the Clinics, held in Freiburg, Germany, on 21-22 June 1999, reviews and discusses the fast-growing knowledge in this field in order to initiate more interdiscliplinary discussions along with new research. Contributors include basic scientists, clinicians of various specialities, morphologists, physiologists, molecular biologists, embryologists, pharmacologists, surgeons, gastroenterologists and behavioural scientists interested in the central and the autonomic nervous system in relation to the gastrointestinal tract.
