This book is about the light like (degenerate) geometry of submanifolds needed to fill a gap in the general theory of submanifolds. The growing importance of light like hypersurfaces in mathematical physics, in particular their extensive use in relativity, and very limited information available on the general theory of lightlike submanifolds, motivated the present authors, in 1990, to do collaborative research on the subject matter of this book. Based on a series of author's papers (Bejancu [3], Bejancu-Duggal [1,3], Dug gal [13], Duggal-Bejancu [1,2,3]) and several other researchers, this volume was conceived and developed during the Fall '91 and Fall '94 visits of Bejancu to the University of Windsor, Canada. The primary difference between the lightlike submanifold and that of its non degenerate counterpart arises due to the fact that in the first case, the normal vector bundle intersects with the tangent bundle of the submanifold. Thus, one fails to use, in the usual way, the theory of non-degenerate submanifolds (cf. Chen [1]) to define the induced geometric objects (such as linear connection, second fundamental form, Gauss and Weingarten equations) on the light like submanifold. Some work is known on null hypersurfaces and degenerate submanifolds (see an up-to-date list of references on pages 138 and 140 respectively). Our approach, in this book, has the following outstanding features: (a) It is the first-ever attempt of an up-to-date information on null curves, lightlike hypersur faces and submanifolds, consistent with the theory of non-degenerate submanifolds.

Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications (Mathematics and Its Applications, 364)

Science & Math

Duggal, Krishan L.

Bejancu, Aurel

Mathematics

Springer

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 special submanifolds such as curves, surfaces, and hypersurfaces. Audience: The book will be of interest to researchers working on pseudo-Finsler geometry in general, and on pseudo-Finsler submanifolds in particular.

Geometry of Pseudo-Finsler Submanifolds (Mathematics and its Applications Volume 527) (Mathematics and Its Applications, 527)

Farran, Hani Reda

Biological Sciences

This self-contained book starts with the basic material on distributions and foliations. It then gradually introduces and builds the tools needed for studying the geometry of foliated manifolds. The main theme of the book is to investigate the interrelations between foliations of a manifold on the one hand, and the many geometric structures that the manifold may admit on the other hand. Among these structures are: affine, Riemannian, semi-Riemannian, Finsler, symplectic, complex and contact structures. Using these structures, the book presents interesting classes of foliations whose geometry is very rich and promising. These include the classes of: Riemannian, totally geodesic, totally umbilical, minimal, parallel non-degenerate, parallel totally - null, parallel partially - null, symmetric, transversally symmetric, Lagrange, totally real and Legendre foliations. Some of these classes appear for the first time in the literature in book form. Finally, the vertical foliation of a vector bundle is used to develop a gauge theory on the total space of a vector bundle.

Foliations and Geometric Structures (Mathematics and Its Applications, Vol. 580)

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can us;; Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Geometry of CR-Submanifolds (Mathematics and its Applications, 23)

Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications (Mathematics and Its Applications)

Duggal, Krishan L. L.

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 special submanifolds such as curves, surfaces, and hypersurfaces.  Audience: The book will be of interest to researchers working on pseudo-Finsler geometry in general, and on pseudo-Finsler submanifolds in particular.

Geometry of Pseudo-Finsler Submanifolds (Mathematics and Its Applications, 527)

See the best price to sell, buy, or rent books by Bejancu, Aurel. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Bejancu, Aurel

See the best price to sell, buy, or rent books by Bejancu, Aurel. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications (Mathematics and Its Applications, 364)

Geometry of Pseudo-Finsler Submanifolds (Mathematics and its Applications Volume 527) (Mathematics and Its Applications, 527)

Foliations and Geometric Structures (Mathematics and Its Applications, Vol. 580)

Geometry of CR-Submanifolds (Mathematics and its Applications, 23)

Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications (Mathematics and Its Applications)

Geometry of Pseudo-Finsler Submanifolds (Mathematics and Its Applications, 527)

Geometry of CR-Submanifolds (Mathematics and its Applications, 23)