Some characterizations of curves and surfaces with density

In the first chapter of this study entitled as "Some Characterizations of Curves and Surfaces with Density" summary of literature has been given about ruled surfaces, rotational surfaces and manifolds with density in Euclidean and Lorentz-Minkowski spaces. In the second chapter, some basic definitions and theorems which will be used in the next chapters have been given. In the third chapter, the curves have been investigated in Euclidean and Lorentz-Minkowski spaces with density e' and the weighted curvatures of these curves have been calculated. The curves with vanishing weighted curvatures have been obtained with the aid of weighted curvatures and by finding the Frenet vectors of these obtaining curves, the Smarandache curves have been constructed. In the fourth chapter, by using the curves which are obtained in the previous chapter, the rotational surfaces and ruled surfaces have been constructed according to density coefficients in Euclidean and Lorentz-Minkowski spaces. Also, some important characterizations have been given for these surfaces and the graphics of them have been drawn. KEYWORDS: Space with Density, Weighted Curvature, Smarandache Curves, Ruled Surfaces, Rotational Surfaces.