Finsler Manifoldunda Esnekliğine Göre Eğrilerin Karakterizasyonları

Yıl 2016, Cilt: 6 Sayı: 3, 119 - 124, 30.09.2016

Alper Osman Öğrenmiş

Öz

Fiziksel olarak, elastik olmayan bir eğri akışı, hareket kaynaklı bir enerji geriliminin bulunmaması olarak
karakterize edilir. Biz bir elastik olmayan düzlem eğrisinin, yani yay uzunluğu her zaman korunan bir eğri için
değişim denklemlerini ortaya çıkardık. Bu çalışmada, elastiklik açısından eğrilerin bazı karakterizasyonları verildi.

Anahtar Kelimeler

Bir eğrinin akışı, finsler manifold, frenet denklemleri

Characterizations of Curves According to Elasticity in Finsler Manifold

Öz

Physically, inelastic curve flow is qualifed by the nonexistence of any strain energy taken from the
motion. We have found out the changing equations for an inelastic curve whose length is preserved over all time.
In this study, we give some characterizations for curves in terms of elasticity

Anahtar Kelimeler

Finsler manifold, flow of a curve, frenet equations

Kaynakça

• Bejancu A, Farran HR, 2000. Geometry of Pseudo-Finsler Submanifolds. Kluwer Academic Pub., First Edition, New York, USA. 241p.
• Brandt EH, 2005. Finslerian quantum feld theory. Nonlinear Analysis, 63: 119-130.
• Gürbüz N, 2009. Inextensible flows of spacelike, timelike and null Curves. International Journal of Contemporary Mathematical Sciences, 4(32): 1599-1604.
• Kwon DY, Park FC, 1999. Evolution of inelastic plane curves. Applied Mathematics Letters. 12: 115-119. Kwon DY, Park FC, Chi DP, 2005. Inextensible flows of curves and developable surfaces. Applied Mathematics Letters. 18: 1156-1162.
• Latif D, Razavi A, 2008. Inextensible Flows of Curves in Minkowskian Space. Advanced Studies in Theoretical Physics. 2(16): 761-768.
• Öğrenmiş AO, Yeneroğlu M, Külahcı M, 2011. Inelastic Admissible Curves in the Pseudo - Galilean Space G31. International Journal of Open Problems Compt. Math. 4(3): 199-207.
• Öztekin H, Bozok HG, 2013. Inextensible flows of curves in 4-dimensional Galilean space G4. Mathematical Sciences and Applications E-Notes, 1(2): 28-34.
• Solange FR, Portugal R, 2001. FINSLER-acomputer algebra package for Finsler geometries. Nonlinear Analysis, 47(9): 6121-6134.
• Yıldız G, Okuyucu OZ, 2014. Inextensible Flows of Curves in Lie Groups. Caspian Journal of Mathematical Sciences, 2(1): 23-32.
• Yılmaz MY, Bektaş M, 2011. Bertrand Curves on Finsler Manifolds. International Journal of Physical and Mathematical Sciences, 2: 5-10.
• Yoon DW, 2011. Inelastic flows of curves according to equiform in Galilean space. Journal of the Chungcheong Mathematical Society, 24(4): 665-673.