Krishan L. Duggal

Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications

Preface. 1. Algebraic Preliminaries. 2. Differential-Geometric Structures on Manifolds. 3. Geometry of Null Curves in Lorentz Manifolds. 4. Lightlike Hypersurfaces of Semi-Riemannian Manifolds. 5. Lightlike Submanifolds of Semi-Riemannian Manifolds. 6. CR-Lightlike Submanifolds of Indefinite Kaehler Manifolds. 7. Lightlike Hypersurfaces of Lorentz Framed Manifolds. 8. Lightlike Hypersurfaces and Electromagnetism. 9. Lightlike Hypersurfaces and General Relativity. References. Author Index. Subject Index.

Null curves and hypersurfaces of semi-Riemannian manifolds

The Concept of Null Curves Null Curves in Lorentzian Manifolds Null Curves in Semi-Riemannian Manifolds Geometry of Null Cartan Curves (Unique Existence Theorems) Applications: Null Soliton Solutions in 3D and 4D Mechanical Systems and 3D Null Curves Lightlike Hypersurfaces Geometry and Physics of Null Geodesics.

Differential Geometry of Lightlike Submanifolds

Preface.- Notations.- 1 Preliminaries.- 2 Lightlike hypersurfaces.- 3 Applications of lightlike hypersurfaces.- 4 Half-lightlike submanifolds.- 5 Lightlike submanifolds.- 6 Submanifolds of indefinite Kahler manifolds.- 7 Submanifolds of indefinite Sasakian manifolds.- 8 Submanifolds of Indefinite quaternion Kahler manifolds.- 9 Applications of lightlike geometry.- Bibliography.- Index.

Lightlike Submanifolds of Indefinite Sasakian Manifolds

We first prove some results on invariant lightlike submanifolds of indefinite Sasakian manifolds. Then, we introduce a general notion of contact Cauchy-Riemann (CR) lightlike submanifolds and study the geometry of leaves of their distributions. We also study a class, namely, contact screen Cauchy-Riemann (SCR) lightlike submanifolds which include invariant and screen real subcases. Finally, we prove characterization theorems on the existence of contact SCR, screen real, invariant, and contact CR minimal lightlike submanifolds.

Symmetries of Spacetimes and Riemannian Manifolds

Dedication. Preface. 1. Preliminaries. 2. Semi-Riemannian Manifolds and Hypersurfaces. 3. Lie Derivatives and Symmetry Groups. 4. Spacetimes of General Relativity. 5. Killing and Affine Killing Vector Fields. 6. Homothetic and Conformal Symmetries. 7. Connection and Curvature Symmetries. 8. Symmetry Inheritance. 9. Symmetries of Some Geometric Structures. A: The Petrov Classification. Bibliography. Index.

Maps Interchanging f-Structures and their Harmonicity

We study some remarkable classes of metric f-structures on differentiable manifolds (namely, almost Hermitian, almost contact, almost S-structures and K-structures). We state and prove the necessary condition(s) for the existence of maps commuting such structures. The paper contains several new results, of geometric significance, on CR-integrable manifolds and the harmonicity of such maps.

Lightlike Submanifolds Of Semi-Riemannian Manifolds

The purpose of this paper is to initiate a study of the differential geometry of lightlike (degenerate) submanifolds of semi-Riemannian manifolds. We construct the transversal vector bundle for an arbitrary lightlike submanifold and obtain results on the geometric structures induced on it.

Constant scalar curvature and warped product globally null manifolds

Abstract This paper deals with the curvature properties of a class of globally null manifolds ( M , g ) which admit a global null vector field and a complete Riemannian hypersurface. Using the warped product technique we study the fundamental problem of finding a warped function such that the degenerate metric g admits a constant scalar curvature on M . Our work has an interplay with the static vacuum solutions of the Einstein equations of general relativity.

Curvature inheritance symmetry in Riemannian spaces with applications to fluid space times

Katzin et al. [G. H. Katzin, J. Levine, and W. R. Davis, J. Math. Phys. 10, 617 (1969)] introduced curvature collineations (CC), defined by a vector ξ, satisfying LξRbcda=0, where Rbcda is the Riemann curvature tensor of a Riemannian space Vn and Lξ denotes the Lie derivative. They proved that a CC is related to a special conformal motion which implies the existence of a covariant constant vector field. Unfortunately, recent study indicates that the existence of a covariant constant vector restricts Vn to a very rare special case with limited physical use. In particular, for a fluid space time with special conformal motion, either stiff or unphysical equations of state are singled out. Moreover, perfect fluid space times do not admit special conformal motions. This information was not available, in 1969, when CC symmetry was introduced. In this paper, CC is generalized to another symmetry called ‘‘curvature inheritance’’ (CI) satisfying LξRbcda=2αRbcda, where α is a scalar function. We prove that a proper...

Conformal collineations and anisotropic fluids in general relativity

Recently, Herrera et al. [L. Herrera, J. Jimenez, L. Leal, J. Ponce de Leon, M. Esculpi, and V. Galino, J. Math. Phys. 25, 3274 (1984)] studied the consequences of the existence of a one‐parameter group of conformal motions for anisotropic matter. They concluded that for special conformal motions, the stiff equation of state (p=μ) is singled out in a unique way, provided the generating conformal vector field is orthogonal to the four‐velocity. In this paper, the same problem is studied by using conformal collineations (which include conformal motions as subgroups). It is shown that, for a special conformal collineation, the stiff equation of state is not singled out. Non‐Einstein Ricci‐recurrent spaces are considered as physical models for the fluid matter.