Geometries on Surfaces [Hardcover]

Both a reference and an introduction on the main results about topological geometries on surfaces.One century after Hilbert constructed the first example of a non-classical affine plane, this book aims to summarize all the major results about geometries on surfaces. Acting both as a reference and a monograph, the authors have include detailed secions on what is known as well as outlining problems that remain to be solved. The authors add interest by giving connections to a host of other areas of maths. This book will appeal to students, researchers and lecturers working in geometry or any one of the many associated areas.One century after Hilbert constructed the first example of a non-classical affine plane, this book aims to summarize all the major results about geometries on surfaces. Acting both as a reference and a monograph, the authors have include detailed secions on what is known as well as outlining problems that remain to be solved. The authors add interest by giving connections to a host of other areas of maths. This book will appeal to students, researchers and lecturers working in geometry or any one of the many associated areas.One century after Hilbert constructed the first example of a non-classical affine plane, this book aims to summarize all the major results about geometries on surfaces. Acting both as a reference and a monograph, the authors have included detailed sections on what is known as well as outlining problems that remain to be solved. There are sections on classical geometries, methods for constructing non-classical geometries and classifications and characterizations of geometries. This work is related to a host of other fields including approximation, convexity, differential geometry topology and many more. This book will appeal to students, researchers and lecturers working in geometry or any one of the many associated areas outlined above.1. Geometries for pedestrians; 2. Flat linear spaces; 3. Spherical circle planes; 4. Toroidal lƒ&