compact manifolds with special holonomy oxford mathematical monographs

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Compact Manifolds With Special Holonomy

Author : Dominic D. Joyce
ISBN : 0198506015
Genre : Mathematics
File Size : 67. 50 MB
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This is a combination of a graduate textbook on Riemannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It is the first book on compact manifolds with exceptional holonomy, and contains much new research material and many new examples.

Special Metrics And Group Actions In Geometry

Author : Simon G. Chiossi
ISBN : 9783319675190
Genre : Mathematics
File Size : 70. 38 MB
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The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

Riemannian Holonomy Groups And Calibrated Geometry

Author : Dominic D. Joyce
ISBN : 9780199215607
Genre : Mathematics
File Size : 61. 52 MB
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Covering an exciting and active area of research at the crossroads of several different fields in mathematics and physics, and drawing on the author's previous work, this text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.

Cohomological Aspects In Complex Non K Hler Geometry

Author : Daniele Angella
ISBN : 9783319024417
Genre : Mathematics
File Size : 46. 45 MB
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In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kähler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kähler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Kähler structure. We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers to study explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered.

Complex And Symplectic Geometry

Author : Daniele Angella
ISBN : 9783319629148
Genre : Mathematics
File Size : 37. 38 MB
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This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

Handbook Of Pseudo Riemannian Geometry And Supersymmetry

Author : Vicente Cortés
ISBN : 3037190795
Genre : Mathematics
File Size : 41. 46 MB
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Lectures On K Hler Manifolds

Author : Werner Ballmann
ISBN : 3037190256
Genre : Mathematics
File Size : 81. 11 MB
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These notes are based on lectures the author held at the University of Bonn and the Erwin-Schrodinger-Institute in Vienna. The aim is to give a thorough introduction to the theory of Kahler manifolds with special emphasis on the differential geometric side of Kahler geometry. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture.

Strings And Geometry

Author : Clay Mathematics Institute. Summer School
ISBN : 082183715X
Genre : Mathematics
File Size : 44. 35 MB
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This volume is the proceedings of the 2002 Clay Mathematics Institute School on Geometry and String Theory. This month-long program was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England, and was organized by both mathematicians and physicists: A. Corti, R. Dijkgraaf, M. Douglas, J. Gauntlett, M. Gross, C. Hull, A. Jaffe and M. Reid. The early part of the school had many lectures that introduced various concepts of algebraic geometry and string theory with a focus on improving communication between these two fields. During the latter part of the program there were also a number of research level talks. This volume contains a selection of expository and research articles by lecturers at the school and highlights some of the current interests of researchers working at the interface between string theory and algebraic geometry. The topics covered include manifolds of special holonomy, supergravity, supersymmetry, D-branes, the McKay correspondence and the Fourier-Mukai transform. The book is suitable for graduate students and research mathematicians interested in relations between mathematical physics and algebraic geometry.

Meteorological Measurement Systems

Author : Fred V. Brock
ISBN : 9780195134513
Genre : Science
File Size : 74. 45 MB
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This book treats instrumentation used in meteorological surface systems, both on the synoptic scale and the mesoscale, and the instrumentation used in upper air soundings. The text includes material on first- and second-order differential equations as applied to instrument dynamic performance, and required solutions are developed. Sensor physics are emphasized in order to explain how sensors work and to explore the strengths and weaknesses of each design type. The book is organized according to sensor type and function (temperature, humidity, and wind sensors, for example), though several unifying themes are developed for each sensor. Functional diagrams are used to portray sensors as a set of logical functions, and static sensitivity is derived from a sensor's transfer equation, focusing attention on sensor physics and on ways in which particular designs might be improved. Sensor performance specifications are explored, helping to compare various instruments and to tell users what to expect as a reasonable level of performance. Finally, the text examines the critical area of environmental exposure of instruments. In a well-designed, properly installed, and well-maintained meteorological measurement system, exposure problems are usually the largest source of error, making this chapter one of the most useful sections of the book.

System Control And Rough Paths

Author : Terry Lyons
ISBN : 0198506481
Genre : Mathematics
File Size : 86. 88 MB
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This book describes a completely novel mathematical development which has already influenced probability theory, and has potential for application to engineering and to areas of pure mathematics. Intended for probabilists, mathematicians and engineers with a mathematical background from graduate level onwards, this book develops the evolution of complex non-linear systems subject to rough or rapidly fluctuating stimuli. Attention is focussed on an analysis of the relationship between the stimulus (or control) and the short to medium term evolution of a receiver (the response of the system). A rapidly fluctuation stimuli can be likened to a huge dataset; and a basic question is how best to reduce this dataset so as to capture the critical information and little else. An essential component problem involves identifying the point at which two different stimuli produce essentially the same response from the class of receivers. (When do two stereo sounds sound the same?). This is an essentially non-linear problem that requires novel mathematics. At one level, this book focuses on systems responding to such rough external stimuli, and demonstrates that the natural reduction approximates the stimuli as a sequence of nilpotent elements. The core result of the book is a continuity theorem that proves that the response of the system depends continuously on these nilpotent elements. A key mathematical aspect of the book is the notion of a rough path, based on combining the notion of p-variation of Wiener with the iterated integral expansions of paths introduced by K. T. Chen. The continuity theorem for these rough paths gives a new way to construct solutions to stochastic differential equations, providing a fresh approach to the Ito theory but also allowing new kinds of noisy perturbations (such as Fractional Brownian Motions) that cannot be discussed in the standard Ito approach. It also provides some interesting concrete examples of 'continuous freegroups'.

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