Affiliation:
1. Department of Mathematics , Sakarya University , 54187 Sakarya , Turkey .
Abstract
Abstract
In this paper, offset ruled surfaces in these spaces are defined by using the geometry of ruled surfaces in Euclidean space with density. The mean curvature and Gaussian curvature of these surfaces are studied. In addition, the relationships between the mean curvature and mean curvature with density, and the Gaussian curvature and the Gaussian curvature with density of the offset ruled surfaces in E
3 with density e
z
and e
−
x
2−
y
2 are given.
Reference16 articles.
1. [1] F. Morgan, Manifolds with Density. Notices of AMS. 52(8) (2005), 853-858.
2. [2] F. Morgan, Myers’ Theorem with Density, Kodai Mathematical Journal. 29(3) (2006), 455-461.10.2996/kmj/1162478772
3. [3] F. Morgan, Manifolds with Density and Perelman’s Proof of the Poincaré Conjecture, The American Mathematical Monthly. 116(2) (2009), 134-142.10.1080/00029890.2009.11920920
4. [4] C. Rosales, A. Canete, On the isoperimetric problem in Euclidean Space with density, Calculus of Variations. 3 (2008), 27-46.
5. [5] I. Corwin, N. Hoffman, S. Hurder, V. Sesum, Y. Xu, Differantial Geometry of Manifolds with Density. Rose-Hulman Undergraduate Mathematics Journal. 7(1) (2006), https://scholar.rose-hulman.edu/rhumj/vol7/iss1/2.
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