Year 2019, Volume 40, Issue 1, Pages 87 - 101 2019-03-22

Minkowski-3 Uzayında Yüzeylerin Razzaboni Dönüşümü Üzerine
On Razzaboni Transformation of Surfaces in Minkowski 3-Space

Melek ERDOĞDU [1] , Mustafa ÖZDEMİR [2]

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Bu çalışmada, Minkowski-3 uzayında, Bertrand eğrilerin binormal hareketi ile meydana gelen, Razzaboni yüzeyi adı verilen yüzeyler incelenmiştir. Minkowski-3 uzayındaki bu yüzeylerin geometrik özelliklerini Bertrand geodeziklerin karakterine bağlı olarak tartıştık. Daha sonra, verilen bir Razzaboni yüzeyi için Razzaboni dönüşümünü tanımladık. Diğer bir deyişle, her durum için Razzaboni yüzeyinin bir duali olduğunu ispatladık. Son olarak, Razzaboni dönüşümlerinin; sabit eğrilikli Bertrand geodeziğe sahip  yüzeyini; işareti ters olmak üzere aynı sabit eğrilikli Bertrand geodeziğe sahip  yüzeyine dönüştürdüğünü gösterdik.

In this paper, we investigate the surfaces generated by binormal motion of Bertrand curves, which is called Razzaboni surface, in Minkowski 3-space. We discussed the geometric properties of these surfaces in  with respect to the character of Bertrand geodesics. Then, we define the Razzaboni transformation for a given Razzaboni surface. In other words, we prove that there exists a dual of Razzaboni surface for each case. Finally, we show that Razzaboni transformation maps the surface  which has Bertrand geodesic with constant curvature, to the surface  whose Bertrand geodesic also has constant curvature with opposite sign.
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Primary Language en
Subjects Basic Sciences
Journal Section Natural Sciences
Authors

Orcid: 0000-0001-9610-6229
Author: Melek ERDOĞDU (Primary Author)
Country: Turkey


Author: Mustafa ÖZDEMİR
Institution: AKDENIZ UNIVERSITY

Bibtex @research article { csj461375, journal = {Cumhuriyet Science Journal}, issn = {2587-2680}, eissn = {2587-246X}, address = {Cumhuriyet University}, year = {2019}, volume = {40}, pages = {87 - 101}, doi = {10.17776/csj.461375}, title = {On Razzaboni Transformation of Surfaces in Minkowski 3-Space}, key = {cite}, author = {ERDOĞDU, Melek and ÖZDEMİR, Mustafa} }
APA ERDOĞDU, M , ÖZDEMİR, M . (2019). On Razzaboni Transformation of Surfaces in Minkowski 3-Space. Cumhuriyet Science Journal, 40 (1), 87-101. DOI: 10.17776/csj.461375
MLA ERDOĞDU, M , ÖZDEMİR, M . "On Razzaboni Transformation of Surfaces in Minkowski 3-Space". Cumhuriyet Science Journal 40 (2019): 87-101 <http://dergipark.gov.tr/csj/issue/43798/461375>
Chicago ERDOĞDU, M , ÖZDEMİR, M . "On Razzaboni Transformation of Surfaces in Minkowski 3-Space". Cumhuriyet Science Journal 40 (2019): 87-101
RIS TY - JOUR T1 - On Razzaboni Transformation of Surfaces in Minkowski 3-Space AU - Melek ERDOĞDU , Mustafa ÖZDEMİR Y1 - 2019 PY - 2019 N1 - doi: 10.17776/csj.461375 DO - 10.17776/csj.461375 T2 - Cumhuriyet Science Journal JF - Journal JO - JOR SP - 87 EP - 101 VL - 40 IS - 1 SN - 2587-2680-2587-246X M3 - doi: 10.17776/csj.461375 UR - https://doi.org/10.17776/csj.461375 Y2 - 2019 ER -
EndNote %0 Cumhuriyet Science Journal On Razzaboni Transformation of Surfaces in Minkowski 3-Space %A Melek ERDOĞDU , Mustafa ÖZDEMİR %T On Razzaboni Transformation of Surfaces in Minkowski 3-Space %D 2019 %J Cumhuriyet Science Journal %P 2587-2680-2587-246X %V 40 %N 1 %R doi: 10.17776/csj.461375 %U 10.17776/csj.461375
ISNAD ERDOĞDU, Melek , ÖZDEMİR, Mustafa . "On Razzaboni Transformation of Surfaces in Minkowski 3-Space". Cumhuriyet Science Journal 40 / 1 (March 2019): 87-101. https://doi.org/10.17776/csj.461375