1,468 research outputs found
Conformal Collineations and Ricci Inheritance Symmetry in String Cloud and String Fluids
Conformal collineations (a generalization of conformal motion) and Ricci
inheritance collineations, defined by , for
string cloud and string fluids in general relativity are studied. By
investigating the kinematical and dynamical properties of such fluids and using
the field equations, some recent studies on the restrictions imposed by
conformal collineations are extended, and new results are found.Comment: 12 pages, LaTeX, no figures, to appear in Int. J. Mod. Phys.
Conformal Ricci collineations of static spherically symmetric spacetimes
Conformal Ricci collineations of static spherically symmetric spacetimes are
studied. The general form of the vector fields generating conformal Ricci
collineations is found when the Ricci tensor is non-degenerate, in which case
the number of independent conformal Ricci collineations is \emph{fifteen}; the
maximum number for 4-dimensional manifolds. In the degenerate case it is found
that the static spherically symmetric spacetimes always have an infinite number
of conformal Ricci collineations. Some examples are provided which admit
non-trivial conformal Ricci collineations, and perfect fluid source of the
matter
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
Hypersurfaces in a conformally flat space with curvature collineation
We classify the shape operators of Einstein and pseudo Einstein hypersurfaces in a
conformally flat space with a symmetry called curvature collineation. We solve the fundamental
problem of finding all possible forms of non-diagonalizable shape operators. A physical example
of space-time with matter is presented to show that the energy condition has direct relation with
the diagonalizability of shape operator
Spacelike Ricci Inheritance Vectors in a Model of String Cloud and String Fluid Stress Tensor
We study the consequences of the existence of spacelike Ricci inheritance
vectors (SpRIVs) parallel to for model of string cloud and string fluid
stress tensor in the context of general relativity. Necessary and sufficient
conditions are derived for a spacetime with a model of string cloud and string
fluid stress tensor to admit a SpRIV and a SpRIV which is also a spacelike
conformal Killing vector (SpCKV). Also, some results are obtained.Comment: 11 page
Ricci Collineations for type B warped space-times
We present the general structure of proper Ricci Collineations (RC) for type
B warped space-times. Within this framework, we give a detailed description of
the most general proper RC for spherically symmetric metrics. As examples,
static spherically symmetric and Friedmann-Robertson-Walker space-times are
considered.Comment: 18 pages, Latex, To appear in GR
- …