Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications write by Krishan L. Duggal. This book was released on 2013-04-17. Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications available in PDF, EPUB and Kindle. 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.
Differential Geometry of Lightlike Submanifolds
Differential Geometry of Lightlike Submanifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry of Lightlike Submanifolds write by Krishan L. Duggal. This book was released on 2011-02-02. Differential Geometry of Lightlike Submanifolds available in PDF, EPUB and Kindle. This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kählerian, Sasakian and quaternion Kähler manifolds.
Pseudo-Riemannian Geometry, [delta]-invariants and Applications
Pseudo-Riemannian Geometry, [delta]-invariants and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Pseudo-Riemannian Geometry, [delta]-invariants and Applications write by Bang-yen Chen. This book was released on 2011. Pseudo-Riemannian Geometry, [delta]-invariants and Applications available in PDF, EPUB and Kindle. The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo-Riemannian submanifolds are also included.The second part of this book is on ë-invariants, which was introduced in the early 1990s by the author. The famous Nash embedding theorem published in 1956 was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, this hope had not been materialized as pointed out by M Gromov in his 1985 article published in Asterisque. The main reason for this is the lack of control of the extrinsic invariants of the submanifolds by known intrinsic invariants. In order to overcome such difficulties, as well as to provide answers for an open question on minimal immersions, the author introduced in the early 1990s new types of Riemannian invariants, known as ë-invariants, which are very different in nature from the classical Ricci and scalar curvatures. At the same time he was able to establish general optimal relations between ë-invariants and the main extrinsic invariants. Since then many new results concerning these ë-invariants have been obtained by many geometers. The second part of this book is to provide an extensive and comprehensive survey over this very active field of research done during the last two decades.
Null Curves And Hypersurfaces Of Semi-riemannian Manifolds
Null Curves And Hypersurfaces Of Semi-riemannian Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Null Curves And Hypersurfaces Of Semi-riemannian Manifolds write by Krishan L Duggal. This book was released on 2007-09-03. Null Curves And Hypersurfaces Of Semi-riemannian Manifolds available in PDF, EPUB and Kindle. This is a first textbook that is entirely focused on the up-to-date developments of null curves with their applications to science and engineering. It fills an important gap in a second-level course in differential geometry, as well as being essential for a core undergraduate course on Riemannian curves and surfaces. The sequence of chapters is arranged to provide in-depth understanding of a chapter and stimulate further interest in the next. The book comprises a large variety of solved examples and rigorous exercises that range from elementary to higher levels. This unique volume is self-contained and unified in presenting:
Geometry of Lightlike Submanifolds
Geometry of Lightlike Submanifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry of Lightlike Submanifolds write by Cyriaque Atindogbé. This book was released on 2012. Geometry of Lightlike Submanifolds available in PDF, EPUB and Kindle. In a recent past, the growing importance of lightlike submanifolds in global Lorentzian geometry and their extensive use in general relativity, motivated their study in a semi-Riemannian manifold. This is the lightlike geometry of (sub-)manifolds where there are significant differences with the nondegenerate case and who make its study slightly more complicated. Indeed, one faces significant technical challenges in their study because conventional techniques known in the nondegenerate case fail. As a consequence, while the geometry of nondegenerate (semi-)Riemannian (sub-)manifolds is almost entirely developed and is well understood, its degenerate counterpart is relatively new and not well explored. So considerable works are needed to fill the gap. The present book falls into this category. It introduces a basic concept: the pseudo-inversion of degenerate metrics which turns out to be decisive whenever the inversion of the metric is required, and we carry out interesting applications. Screen conformal normalization along with Einstein condition are studied. For lightlike isotropic submanifolds, we consider the problem of reduction of codimension.
