Krishan L Duggal's Books

Null Curves and Hypersurfaces of Semi-Riemannian Manifolds

By: Krishan L. Duggal,Dae Ho Jin

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Null Curves and Hypersurfaces of Semi-Riemannian Manifolds

By: Krishan L. Duggal,Dae Ho Jin

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: ? A systematic account of all possible null curves, their Frenet equations, unique null Cartan curves in Lorentzian manifolds and their practical problems in science and engineering.? The geometric and physical significance of null geodesics, mechanical systems involving curvature of null curves, simple variation problems and the interrelation of null curves with hypersurfaces.

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Page Count

302

Publisher

World Scientific

Published Date

ISBN 10

981270647X

ISBN 13

9789812706478

Symmetries of Spacetimes and Riemannian Manifolds

By: Krishan L. Duggal,Ramesh Sharma

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Symmetries of Spacetimes and Riemannian Manifolds

By: Krishan L. Duggal,Ramesh Sharma

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.

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Page Count

227

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461553156

ISBN 13

9781461553151

Differential Geometry of Lightlike Submanifolds

By: Krishan L. Duggal,Bayram Sahin

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Differential Geometry of Lightlike Submanifolds

By: Krishan L. Duggal,Bayram Sahin

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.

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Page Count

484

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3034602510

ISBN 13

9783034602518

Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications

By: Krishan L. Duggal,Aurel Bejancu

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Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications

By: Krishan L. Duggal,Aurel Bejancu

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.

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Page Count

311

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401720894

ISBN 13

9789401720892

Foliations in Cauchy-Riemann Geometry

By: Elisabetta Barletta,Sorin Dragomir,Krishan L. Duggal

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Foliations in Cauchy-Riemann Geometry

By: Elisabetta Barletta,Sorin Dragomir,Krishan L. Duggal

The authors study the relationship between foliation theory and differential geometry and analysis on Cauchy-Riemann (CR) manifolds. The main objects of study are transversally and tangentially CR foliations, Levi foliations of CR manifolds, solutions of the Yang-Mills equations, tangentially Monge-Ampere foliations, the transverse Beltrami equations, and CR orbifolds. The novelty of the authors' approach consists in the overall use of the methods of foliation theory and choice of specific applications. Examples of such applications are Rea's holomorphic extension of Levi foliations, Stanton's holomorphic degeneracy, Boas and Straube's approximately commuting vector fields method for the study of global regularity of Neumann operators and Bergman projections in multi-dimensional complex analysis in several complex variables, as well as various applications to differential geometry. Many open problems proposed in the monograph may attract the mathematical community and lead to further applications of

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Page Count

270

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821843044

ISBN 13

9780821843048

Recent Advances in Riemannian and Lorentzian Geometries

By: Krishan L. Duggal,Ramesh Sharma

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Recent Advances in Riemannian and Lorentzian Geometries

By: Krishan L. Duggal,Ramesh Sharma

This volume covers material presented by invited speakers at the AMS special session on Riemannian and Lorentzian geometries held at the annual Joint Mathematics Meetings in Baltimore. Topics covered include classification of curvature-related operators, curvature-homogeneous Einstein 4-manifolds, linear stability/instability singularity and hyperbolic operators of spacetimes, spectral geometry of holomorphic manifolds, cut loci of nilpotent Lie groups, conformal geometry of almost Hermitian manifolds, and also submanifolds of complex and contact spaces. This volume can serve as a good reference source and provide indications for further research. It is suitable for graduate students and research mathematicians interested in differential geometry.

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Page Count

214

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821833790

ISBN 13

9780821833797

Differential Geometry and Mathematical Physics

By: John K. Beem,Krishan L. Duggal,American Mathematical Society,Canadian Mathematical Society

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Differential Geometry and Mathematical Physics

By: John K. Beem,Krishan L. Duggal,American Mathematical Society,Canadian Mathematical Society

This book contains the proceedings of the Special Session, Geometric Methods in Mathematical Physics, held at the joint AMS-CMS meeting in Vancouver in August 1993. The papers collected here contain a number of new results in differential geometry and its applications to physics. The major themes include black holes, singularities, censorship, the Einstein field equations, geodesics, index theory, submanifolds, CR-structures, and space-time symmetries. In addition, there are papers on Yang-Mills fields, geometric techniques in control theory, and equilibria. Containing new results by established researchers in the field, this book provides a look at developments in this exciting area of research.

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