Lightlike Submanifolds Of Semi Riemannian Manifolds And Applications

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Lightlike Submanifolds Of Semi Riemannian Manifolds And Applications

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Author : Krishan Duggal
language : en
Publisher:
Release Date : 2014-01-15

Lightlike Submanifolds Of Semi Riemannian Manifolds And Applications written by Krishan Duggal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Lightlike Submanifolds Of Semi Riemannian Manifolds And Applications

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Author : Krishan L. Duggal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Lightlike Submanifolds Of Semi Riemannian Manifolds And Applications written by Krishan L. Duggal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

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

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Author : Krishan L. Duggal
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-02

Differential Geometry Of Lightlike Submanifolds written by Krishan L. Duggal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-02 with Mathematics categories.

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.

Structures On Manifolds

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Author : Masahiro Kon
language : en
Publisher: World Scientific
Release Date : 1985-02-01

Structures On Manifolds written by Masahiro Kon and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-02-01 with categories.

Contents: Riemannian ManifoldsSubmanifolds of Riemannian ManifoldsComplex ManifoldsSubmanifolds of Kaehlerian ManifoldsContact ManifoldsSubmanifolds of Sasakian Manifoldsf-StructuresProduct ManifoldsSubmersions Readership: Mathematicians. Keywords:Riemannian Manifold;Submanifold;Complex Manifold;Contact Manifold;Kaehlerian Manifold;Sasakian Manifold;Anti-Invariant Submanifold;CR Submanifold;Contact CR Submanifold;Submersion

Null Curves And Hypersurfaces Of Semi Riemannian Manifolds

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Author : Krishan L Duggal
language : en
Publisher: World Scientific Publishing Company
Release Date : 2007-09-03

Null Curves And Hypersurfaces Of Semi Riemannian Manifolds written by Krishan L Duggal and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-03 with Mathematics categories.

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:

Semi Riemannian Geometry With Applications To Relativity

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Author : Barrett O'Neill
language : en
Publisher: Academic Press
Release Date : 1983-07-29

Semi Riemannian Geometry With Applications To Relativity written by Barrett O'Neill and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-07-29 with Mathematics categories.

This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.

Mathematical Methods And Modelling In Applied Sciences

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Author : Mehmet Zeki Sarıkaya
language : en
Publisher: Springer Nature
Release Date : 2020-03-02

Mathematical Methods And Modelling In Applied Sciences written by Mehmet Zeki Sarıkaya and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-02 with Technology & Engineering categories.

This book presents a collection of original research papers from the 2nd International Conference on Mathematical and Related Sciences, held in Antalya, Turkey, on 27 – 30 April 2019 and sponsored/supported by Düzce University, Turkey; the University of Jordan; and the Institute of Applied Mathematics, Baku State University, Azerbaijan. The book focuses on various types of mathematical methods and models in applied sciences; new mathematical tools, techniques and algorithms related to various branches of applied sciences; and important aspects of applied mathematical analysis. It covers mathematical models and modelling methods related to areas such as networks, intelligent systems, population dynamics, medical science and engineering, as well as a wide variety of analytical and numerical methods. The conference aimed to foster cooperation among students, researchers and experts from diverse areas of mathematics and related sciences and to promote fruitful exchanges on crucial research in the field. This book is a valuable resource for graduate students, researchers and educators interested in applied mathematics and interactions of mathematics with other branches of science to provide insights into analysing, modelling and solving various scientific problems in applied sciences.

Lorentzian Geometry And Related Topics

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Author : María A. Cañadas-Pinedo
language : en
Publisher: Springer
Release Date : 2018-03-06

Lorentzian Geometry And Related Topics written by María A. Cañadas-Pinedo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-06 with Mathematics categories.

This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathematics and physics. This book is addressed to differential geometers, mathematical physicists and relativists, and graduate students interested in the field.

Geometry Of Submanifolds And Applications

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Author : Bang-Yen Chen
language : en
Publisher: Springer Nature
Release Date : 2024-03-26

Geometry Of Submanifolds And Applications written by Bang-Yen Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-26 with Mathematics categories.

This book features chapters written by renowned scientists from various parts of the world, providing an up-to-date survey of submanifold theory, spanning diverse topics and applications. The book covers a wide range of topics such as Chen–Ricci inequalities in differential geometry, optimal inequalities for Casorati curvatures in quaternion geometry, conformal η-Ricci–Yamabe solitons, submersion on statistical metallic structure, solitons in f(R, T)-gravity, metric-affine geometry, generalized Wintgen inequalities, tangent bundles, and Lagrangian submanifolds. Moreover, the book showcases the latest findings on Pythagorean submanifolds and submanifolds of four-dimensional f-manifolds. The chapters in this book delve into numerous problems and conjectures on submanifolds, providing valuable insights for scientists, educators, and graduate students looking to stay updated with the latest developments in the field. With its comprehensive coverage and detailed explanations, this book is an essential resource for anyone interested in submanifold theory.

Symmetries Of Spacetimes And Riemannian Manifolds

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Author : Krishan L. Duggal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22

Symmetries Of Spacetimes And Riemannian Manifolds written by Krishan L. Duggal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Mathematics categories.

This book provides an upto date information on metric, connection and curva ture symmetries used in geometry and physics. More specifically, we present the characterizations and classifications of Riemannian and Lorentzian manifolds (in particular, the spacetimes of general relativity) admitting metric (i.e., Killing, ho mothetic and conformal), connection (i.e., affine conformal and projective) and curvature symmetries. Our approach, in this book, has the following outstanding features: (a) It is the first-ever attempt of a comprehensive collection of the works of a very large number of researchers on all the above mentioned symmetries. (b) We have aimed at bringing together the researchers interested in differential geometry and the mathematical physics of general relativity by giving an invariant as well as the index form of the main formulas and results. (c) Attempt has been made to support several main mathematical results by citing physical example(s) as applied to general relativity. (d) Overall the presentation is self contained, fairly accessible and in some special cases supported by an extensive list of cited references. (e) The material covered should stimulate future research on symmetries. Chapters 1 and 2 contain most of the prerequisites for reading the rest of the book. We present the language of semi-Euclidean spaces, manifolds, their tensor calculus; geometry of null curves, non-degenerate and degenerate (light like) hypersurfaces. All this is described in invariant as well as the index form.