A brief summary of results on kinematic self-similarities in general relativity is given. Attention is then focused on locally rotationally symmetric models, and coordinate expressions for the metric and the kinematic self-similar vectors are provided. Einstein's field equations for perfect fluid models are investigated and all the homothetic perfect fluid solutions admitting a maximal four-par...

Using the Schwarz function of an ellipse, it was recently shown that galaxies with density constant on confocal ellipses can produce at most four “bright” images of a single source. The more physically interesting example of an isothermal galaxy has density that is constant on homothetic ellipses. In that case bright images can be seen to correspond to zeros of a certain transcendental harmonic...

We give an exact solution of the 5D Einstein equations which in 4D can be interpreted as a spherically symmetric distribution of matter, whose effective density and pressure are nonstatic, nonuniform, and satisfy the equation of state of radiation. The solution admits a homothetic Killing vector in 5D, which induces the existence of self-similar symmetry in 4D, where the line element as well as...

introduction: the use of multiple cameras for motion analysis and single joint motion is very difficult and needs high technology in laboratory conditions. detection of single joint motion in kinesthesia and analysis of its changes can be done by one camera at one direction. in this study, we present the validity and reliability of a new prototype simulator system used for motion analysis appli...

We prove the theorem valid for (Pseudo)-Riemannian manifolds V n : "Let x 2 V n be a xed point of a homothetic motion which is not an isometry then all curvature invariants vanish at x." and get the Corollary: "All curvature invariants of the plane wave metric ds 2 = 2 du dv + a 2 (u) dw 2 + b 2 (u) dz 2 identically vanish." Analysing the proof we see: The fact that for deenite signature atness...

Consider a properly immersed minimal surface M in R with area A(r) in balls B(r) of radius r centered at the origin. By the monotonicity formula, the function A(r) = A(r) r2 is monotonically increasing. We say that M has area growth constant A(M) ∈ (0,∞], if A(M) = limr→∞A(r). Note that under a rigid motion or homothety M ′ of M , the number A(M) = A(M ′), and so, A(M) ≥ π, which is the area gr...

We prove the theorem valid for (Pseudo)-Riemannian manifolds Vn: ”Let x ∈ Vn be a fixed point of a homothetic motion which is not an isometry then all curvature invariants vanish at x.” and get the Corollary: ”All curvature invariants of the plane wave metric ds = 2 du dv + a(u) dw + b(u) dz identically vanish.” Analysing the proof we see: The fact that for definite signature flatness can be ch...

In this paper, we state some geometric properties of conformal quasi-hemi-slant Riemannian maps from almost Hermitian manifolds to manifolds. We give necessary and sufficient conditions for certain distributions be integrable get examples. For such distributions, examine which define totally geodesic foliations on base manifold. addition, apply notion pluriharmonicity relations between horizont...