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.
Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications
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.
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.
Contact Geometry of Slant Submanifolds
Contact Geometry of Slant 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 Contact Geometry of Slant Submanifolds write by Bang-Yen Chen. This book was released on 2022-06-27. Contact Geometry of Slant Submanifolds available in PDF, EPUB and Kindle. This book contains an up-to-date survey and self-contained chapters on contact slant submanifolds and geometry, authored by internationally renowned researchers. The notion of slant submanifolds was introduced by Prof. B.Y. Chen in 1990, and A. Lotta extended this notion in the framework of contact geometry in 1996. Numerous differential geometers have since obtained interesting results on contact slant submanifolds. The book gathers a wide range of topics such as warped product semi-slant submanifolds, slant submersions, semi-slant ξ┴ -, hemi-slant ξ┴ -Riemannian submersions, quasi hemi-slant submanifolds, slant submanifolds of metric f-manifolds, slant lightlike submanifolds, geometric inequalities for slant submanifolds, 3-slant submanifolds, and semi-slant submanifolds of almost paracontact manifolds. The book also includes interesting results on slant curves and magnetic curves, where the latter represents trajectories moving on a Riemannian manifold under the action of magnetic field. It presents detailed information on the most recent advances in the area, making it of much value to scientists, educators and graduate students.
The Geometry of Submanifolds
The Geometry of 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 The Geometry of Submanifolds write by Yu. Aminov. This book was released on 2001-01-11. The Geometry of Submanifolds available in PDF, EPUB and Kindle. This is a comprehensive presentation of the geometry of submanifolds that expands on classical results in the theory of curves and surfaces. The geometry of submanifolds starts from the idea of the extrinsic geometry of a surface, and the theory studies the position and properties of a submanifold in ambient space in both local and global aspects. Discussions include submanifolds in Euclidean states and Riemannian space, minimal submanifolds, Grassman mappings, multi-dimensional regular polyhedra, and isometric immersions of Lobachevski space into Euclidean spaces. This volume also highlights the contributions made by great geometers to the geometry of submanifolds and its areas of application.
