Download or read book Aspects of Differential Geometry IV written by Esteban Calviño-Louzao and published by Springer Nature. This book was released on 2022-06-01 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book IV continues the discussion begun in the first three volumes. Although it is aimed at first-year graduate students, it is also intended to serve as a basic reference for people working in affine differential geometry. It also should be accessible to undergraduates interested in affine differential geometry. We are primarily concerned with the study of affine surfaces {which} are locally homogeneous. We discuss affine gradient Ricci solitons, affine Killing vector fields, and geodesic completeness. Opozda has classified the affine surface geometries which are locally homogeneous; we follow her classification. Up to isomorphism, there are two simply connected Lie groups of dimension 2. The translation group R2 is Abelian and the + group\index{ax+b group} is non-Abelian. The first chapter presents foundational material. The second chapter deals with Type surfaces. These are the left-invariant affine geometries on R2. Associating to each Type surface the space of solutions to the quasi-Einstein equation corresponding to the eigenvalue =-1$ turns out to be a very powerful technique and plays a central role in our study as it links an analytic invariant with the underlying geometry of the surface. The third chapter deals with Type surfaces; these are the left-invariant affine geometries on the + group. These geometries form a very rich family which is only partially understood. The only remaining homogeneous geometry is that of the sphere 2. The fourth chapter presents relations between the geometry of an affine surface and the geometry of the cotangent bundle equipped with the neutral signature metric of the modified Riemannian extension.
Download or read book Algebraic Geometry IV written by A.N. Parshin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory, by well-known experts in the fields. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.
Download or read book Geometry IV written by Yurĭi Grigorevǐc Reshetnyak and published by Springer Science & Business Media. This book was released on 1993-10-14 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains two surveys on modern research into non-regular Riemannian geometry, carried out mostly by Russian mathematicians. Coverage examines two-dimensional Riemannian manifolds of bounded curvature and metric spaces whose curvature lies between two given constants. This book will be immensely useful to graduate students and researchers in geometry, in particular Riemannian geometry.
Download or read book A School Geometry written by Henry Sinclair Hall and published by . This book was released on 1908 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book General Catalog written by University of Missouri and published by . This book was released on 1873 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Year Book written by Hope College and published by . This book was released on 1901 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Catalogue written by Phillips Academy and published by . This book was released on 1901 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Catalogue written by Grand Island College and published by . This book was released on 1906 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamical Systems IV written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes a snapshot of the mathematical foundations of classical and quantum mechanics from a contemporary mathematical viewpoint. It covers a number of important recent developments in dynamical systems and mathematical physics and places them in the framework of the more classical approaches; the presentation is enhanced by many illustrative examples concerning topics which have been of especial interest to workers in the field, and by sketches of the proofs of the major results. The comprehensive bibliographies are designed to permit the interested reader to retrace the major stages in the development of the field if he wishes. Not so much a detailed textbook for plodding students, this volume, like the others in the series, is intended to lead researchers in other fields and advanced students quickly to an understanding of the 'state of the art' in this area of mathematics. As such it will serve both as a basic reference work on important areas of mathematical physics as they stand today, and as a good starting point for further, more detailed study for people new to this field.
Download or read book Vector Geometry written by Gilbert de B. Robinson and published by Courier Corporation. This book was released on 2013-10-10 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962 edition.
Download or read book Information Geometry and Its Applications written by Shun-ichi Amari and published by Springer. This book was released on 2016-02-02 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
Download or read book Report of the Board of Education to the Commissioners of the District of Columbia written by District of Columbia. Board of Education and published by . This book was released on 1906 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Report written by District of Columbia. Board of Education and published by . This book was released on 1904 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Report of the Commissioners of the District of Columbia written by District of Columbia. Board of Commissioners and published by . This book was released on 1904 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Journal of the Florida Education Association written by Florida Education Association and published by . This book was released on 1926 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Catalogue of Oberlin College for the Year written by Oberlin College and published by . This book was released on 1915 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Annual Reports of the President and the Treasurer written by Oberlin College and published by . This book was released on 1913 with total page 1262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
