scholarly journals On Pseudospherical Smarandache Curves in Minkowski 3-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Esra Betul Koc Ozturk ◽  
Ufuk Ozturk ◽  
Kazim Ilarslan ◽  
Emilija Nešović
Keyword(s):  
Geodesic Curvature ◽  
Spacelike Curve ◽  
Constant Geodesic Curvature ◽  
Straight Lines

In this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space. We obtain the geodesic curvature and the expressions for the Sabban frame’s vectors of spacelike and timelike pseudospherical Smarandache curves. We also prove that if the pseudospherical null straight lines are the Smarandache curves of a spacelike pseudospherical curveα, thenαhas constant geodesic curvature. Finally, we give some examples of pseudospherical Smarandache curves.

scholarly journals Submersions and curves of constant geodesic curvature

2019 ◽  
Vol 292 (9) ◽  
pp. 1956-1971
Author(s):  
M. Godoy Molina ◽  
E. Grong ◽  
I. Markina
Keyword(s):  
Geodesic Curvature ◽  
Constant Geodesic Curvature

scholarly journals On k-type spacelike slant helices lying on lightlike surfaces

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2781-2796
Author(s):  
Ufuk Öztürk ◽  
Emilija Nesovic ◽  
Öztürk Koç
Keyword(s):  
Minkowski Space ◽  
Sufficient Conditions ◽  
Geodesic Curvature ◽  
Normal Curvature ◽  
Spacelike Curve ◽  
Bishop Frame ◽  
Darboux Frame

In this paper, we define k-type spacelike slant helices lying on a lightlike surface in Minkowski space E31 according to their Darboux frame for k ? {0,1,2}. We obtain the necessary and the sufficient conditions for spacelike curves with non-null and null principal normal lying on lightlike surface to be the k-type spacelike slant helices in terms of their geodesic curvature, normal curvature and geodesic torsion. Additionally, we determine their axes and show that the Darboux frame of a spacelike curve lying on a lightlike surface coincides with its Bishop frame if and only if it has zero geodesic torsion. Finally, we give some examples.

Domain Formation in Synthetic Quartz

1971 ◽  
Vol 29 ◽  
pp. 156-157
Author(s):  
Joseph J. Comer
Keyword(s):  
Electron Beam ◽  
Room Temperature ◽  
Domain Formation ◽  
Synthetic Quartz ◽  
Transmission Electron ◽  
Black Spots ◽  
Diffraction Mode ◽  
Domain Boundaries ◽  
Kikuchi Lines ◽  
Straight Lines

Domains visible by transmission electron microscopy, believed to be Dauphiné inversion twins, were found in some specimens of synthetic quartz heated to 680°C and cooled to room temperature. With the electron beam close to parallel to the [0001] direction the domain boundaries appeared as straight lines normal to <100> and <410> or <510> directions. In the selected area diffraction mode, a shift of the Kikuchi lines was observed when the electron beam was made to traverse the specimen across a boundary. This shift indicates a change in orientation which accounts for the visibility of the domain by diffraction contrast when the specimen is tilted. Upon exposure to a 100 KV electron beam with a flux of 5x 1018 electrons/cm2sec the boundaries are rapidly decorated by radiation damage centers appearing as black spots. Similar crystallographio boundaries were sometimes found in unannealed (0001) quartz damaged by electrons.

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