Adi diferansiyel denklemler ve riemann yapısı
Küçük Resim Yok
Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Trakya Üniversitesi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Bu tez çalışmasında birinci ve ikinci mertebeden adi differansiyel denklemle- rin tanımladığı manifoldların eğrilik özellikleri Riemann geometrisi anlamında ince- lenmiş ve adi diferansiyel denklemlerin eşdeğerlik problemi denklemlerin tanımladığı Riemann manifoldları üzerinde denklemleri temsil eden eşçatıların O(n, R)-değerli eş- değerlik problemi olarak ele alınmıştır. Bu amaçla birinci ve ikinci mertebeden adi di- feransiyel denklemler sırasıyla uygun jet uzayları içinde birer manifold olarak ele alınarak denklemleri temsil eden dış diferansiyel sistemlerin elemanları ile bu manifoldlar üzerinde Riemann metrikleri tanımlanmıştır.
The aim of this thesis is to examine the curvature properties of manifolds, defined by first and second order ordinary differential equations, in terms of Riemannian geometry and the equivalent problem of differential equations, defined on Riemannian manifolds, is treated as the O(n, R)-valued equivalence problem formed by canonical contact forms representing equations and their equivalence classes constructed with the independence condition.For this purpose, first and second-order ordinary differential equations are res- pectively considered as manifolds within the jet spaces Riemannian metrics have been defined along with elements of exterior differential systems representing the equations within these manifolds.
The aim of this thesis is to examine the curvature properties of manifolds, defined by first and second order ordinary differential equations, in terms of Riemannian geometry and the equivalent problem of differential equations, defined on Riemannian manifolds, is treated as the O(n, R)-valued equivalence problem formed by canonical contact forms representing equations and their equivalence classes constructed with the independence condition.For this purpose, first and second-order ordinary differential equations are res- pectively considered as manifolds within the jet spaces Riemannian metrics have been defined along with elements of exterior differential systems representing the equations within these manifolds.
Açıklama
Yüksek Lisans
Anahtar Kelimeler
Matematik, Mathematics
