Pointwise 1-Type Gauss Map os Developable Smarandache Rules Surfaces
Title | Pointwise 1-Type Gauss Map os Developable Smarandache Rules Surfaces PDF eBook |
Author | Stuti Tamta |
Publisher | Infinite Study |
Pages | 19 |
Release | 2023-01-01 |
Genre | Mathematics |
ISBN |
In this paper, we study the developable TN, TB, and NB-Smarandache ruled surface with a pointwise 1-type Gauss map. In particular, we obtain that every developable TN-Smarandache ruled surface has constant mean curvature, and every developable TB-Smarandache ruled surface is minimal if and only if the curve is a place curve with non-zero curvature or a helix, and every developable NB-Smarandache ruled surface is always plane. We also provide some examples.
The Geometry of the Generalized Gauss Map
Title | The Geometry of the Generalized Gauss Map PDF eBook |
Author | David A. Hoffman |
Publisher | American Mathematical Soc. |
Pages | 113 |
Release | 1980 |
Genre | Mathematics |
ISBN | 0821822365 |
This paper is devoted primarily to the study of properties of the Grassmannian of oriented 2-planes in [double-struck capital]R[superscript]n and to applications of these properties to understanding minimal surfaces in [double-struck capital]R[superscript]n via the generalized Gauss map. The extrinsic geometry of the Grassmannian, when considered as a submanifold of [double-struck capital]CP[superscript]n-2, is investigated, with special emphasis on the nature of the intersection of the Grassmannian with linear subspaces of [double-struck capital]CP[superscript]n-1. These results are the basis for a discussion of minimal surfaces that are degenerate in various ways; understanding the different types of degeneracy and their interrelations is a critical step toward obtaining a clear picture of the basic geometric properties of minimal surfaces in [double-struck capital]R[superscript]n.
Special Smarandache Ruled Surfaces According to Flc Frame
Title | Special Smarandache Ruled Surfaces According to Flc Frame PDF eBook |
Author | Suleyman Senyurt |
Publisher | Infinite Study |
Pages | 18 |
Release | 2023-01-01 |
Genre | Mathematics |
ISBN |
In this study, we introduce some special ruled surfaces according to the Flc frame of a given polynomial curve. We name these ruled surfaces as Smarandache ruled surfaces and provide their characteristics such as Gauss and mean curvatures in order to specify their developability and minimality conditions. Moreover, we examine the conditions if the parametric curves of the surfaces are asymptotic, geodesic or curvature line. Such conditions are also argued in terms of the developability and minimality conditions. Finally, we give an example and picture the corresponding graphs of ruled surfaces by using Maple17.
Ruled Surfaces with Gauss Map of Finite Type
Title | Ruled Surfaces with Gauss Map of Finite Type PDF eBook |
Author | Thomas Hasanis |
Publisher | |
Pages | 18 |
Release | 1992 |
Genre | |
ISBN |
The Gauss Map of Spacelike Surfaces in $ R_ P^ {2+p1} $
Title | The Gauss Map of Spacelike Surfaces in $ R_ P^ {2+p1} $ PDF eBook |
Author | Chen Weihuan |
Publisher | |
Pages | 6 |
Release | 1996 |
Genre | |
ISBN |
Cusps of Gauss Mappings
Title | Cusps of Gauss Mappings PDF eBook |
Author | Thomas Banchoff |
Publisher | Pitman Advanced Publishing Program |
Pages | 104 |
Release | 1982 |
Genre | Mathematics |
ISBN |
Ruled Surfaces and Tubes with Finite Type Gauss Maps
Title | Ruled Surfaces and Tubes with Finite Type Gauss Maps PDF eBook |
Author | Christos Baikoussis |
Publisher | |
Pages | 24 |
Release | 1992 |
Genre | |
ISBN |