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.
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.
Energies with Constant Mean Curvature of Tubular Surfaces by Bishop Frame
Yıl 2021,
Cilt: 21 Sayı: 6, 1324 - 1329, 31.12.2021
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.
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.
Ertem Kaya, F. (2021). Energies with Constant Mean Curvature of Tubular Surfaces by Bishop Frame. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 21(6), 1324-1329. https://doi.org/10.35414/akufemubid.977234
AMA
Ertem Kaya F. Energies with Constant Mean Curvature of Tubular Surfaces by Bishop Frame. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. Aralık 2021;21(6):1324-1329. doi:10.35414/akufemubid.977234
Chicago
Ertem Kaya, Filiz. “Energies With Constant Mean Curvature of Tubular Surfaces by Bishop Frame”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 21, sy. 6 (Aralık 2021): 1324-29. https://doi.org/10.35414/akufemubid.977234.
EndNote
Ertem Kaya F (01 Aralık 2021) Energies with Constant Mean Curvature of Tubular Surfaces by Bishop Frame. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 21 6 1324–1329.
IEEE
F. Ertem Kaya, “Energies with Constant Mean Curvature of Tubular Surfaces by Bishop Frame”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 21, sy. 6, ss. 1324–1329, 2021, doi: 10.35414/akufemubid.977234.
ISNAD
Ertem Kaya, Filiz. “Energies With Constant Mean Curvature of Tubular Surfaces by Bishop Frame”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 21/6 (Aralık 2021), 1324-1329. https://doi.org/10.35414/akufemubid.977234.
JAMA
Ertem Kaya F. Energies with Constant Mean Curvature of Tubular Surfaces by Bishop Frame. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2021;21:1324–1329.
MLA
Ertem Kaya, Filiz. “Energies With Constant Mean Curvature of Tubular Surfaces by Bishop Frame”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 21, sy. 6, 2021, ss. 1324-9, doi:10.35414/akufemubid.977234.
Vancouver
Ertem Kaya F. Energies with Constant Mean Curvature of Tubular Surfaces by Bishop Frame. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2021;21(6):1324-9.