Sabit Ortalama Eğrilikli Bishop Çatılı Tubular Yüzeylerin Enerjileri

Yıl 2021, , 1324 - 1329, 31.12.2021

Filiz Ertem Kaya

https://doi.org/10.35414/akufemubid.977234

Cited By: 1

Öz

Bu makalede μ : M → G Öklid metrikli Bishop çatılı Tubular yüzeylerin Helfrich ve Willmore enerjileri hesaplandı and Bishop çatılı Tubular yüzeylerin Helfrich ve Willmore enerjilerinin bulunmasında ve bazı teoremlerin verilmesinde diferensiyel geometrideki eğriliklerinin ne denli önemli olduğu görüldü. Bu hesaplamalar her ne kadar diferensiyel geometri için eğriliklerin önemli olduğunu ispatlasa da de aslında bu hesaplamalar matematiksel fizik için de önem arz etmektedir.

Anahtar Kelimeler

Tubular yüzeyler, Eğrilikler, Bishop çatısı, Willmore enerji

Destekleyen Kurum

yok

Proje Numarası

yok

Energies with Constant Mean Curvature of Tubular Surfaces by Bishop Frame

Öz

In this paper Euclidean metric induced by μ : M → G be the mean curvature of Tubular surfaces by Bishop frame are computed and the curvatures in differential geometry that are so important for computing the Helfrich and Willmore energy of the tubular surfaces by bishop frame and giving some theorems are seen. Even though these calculations are very important to prove that the curvatures are very important in differential geometry, in actually these calculations are clearly important as mathematical physics.

Anahtar Kelimeler

Tubular surfaces, Curvature, Bishop frame, Willmore energy

Proje Numarası

yok

Kaynakça

• Bishop, R. L., 1975. There is no more than one way to frame a curve, American Mathematical Monthly, 82 (3), 246-251.
• Doğan, F. and Yaylı, Y., 2011. On the tubular surface with Bishop frame, Commun. Fac. Sci. Univ. Ank. SeriesA1, 60 (1), 59-69.
• Doğan, F. 2012. A note on Tubes, International Journal of physical and Mathematical Sciences, 3 (1), 98-105.
• Doğan, F. and Yaylı, Y. 2012. Tubes with darboux frame, Int J. Contemp. Math. Sciences, 7 (16), 751-758.
• Gray, A., 2005. Modern Differential Geometry of Curves and Surfaces with Matematica, Third Edition by Elsa Abbana and Simon Salamon, 821-927.
• Karsten, G.-B., 2012. Triply periodic Minimal and Constant Mean curvature Surfaces, Interfaces Focus; 2, 582-588.
• Kişi İ., Öztürk, G., 2017. A new approach to canal surface with parallel transport frame, International Journal of Geometric Methods in Modern Physics, 14(2), 1750026.
• Liu, Bing, Sclabassi, R.J., Liu, Qiang, Kassam, A., Li, ChingChung, Sun, Mingui, 2005. Detection of region of interest in neurosurgical video used for telemedicine, 2005 IEEE International Conference on Information Acquisition.
• Willmore, T. J., 1959. Introduction to Differential Geometry, Clarendon, Oxford, 128.
• Willmore, T. J., 1965. Note on embedded surfaces, An. Sti. Univ. Al. Cusa Iasi, N. Ser., Sect. la Mat. 11B, 493-496.