Anholonomik Koordinatlar Boyunca Yönlü Enerji Fonksiyonelleri

Abstract

Bu makalede 3-boyutlu Öklid uzayında bazı özel yönlü enerji fonksiyonelleri birim vektör alanlarının yönlü enerjileri ve pseudo-açıları hesaplanarak incelenmiştir. Bu yaklaşımdan hareketle hız vektörlerinin yönlü enerji fonksiyonellerince belirlenen kritik noktaları tanımlanmıştır. Daha sonra yönlü enerji fonksiyonellerinin ekstremum değerleri ve harmonik dönüşümleri için bazı şartlar tartışılmıştır. Sonuç olarak, vektör alanlarının total eğrilmesi veya enerjisi olarak bilinen kavramları genelleştirecek şekilde eğrilik vektör alanının yönlü harmonik ve biharmonik denklemleri tanımlanmıştır.

Keywords

• Yönlü enerji fonksiyoneli
• yönlü enerji minimizesi
• harmoniklik ve biharmoniklik

Directional Energy Functionals Through Anholonomic Coordinates

Abstract

In this paper, a special case of directional energy functional is investigated by computing the directional energy and pseudoangle of unit vector fields in the ordinary three-dimensional space. This approach is also extended simultaneously to define the critical points of the directional energy functionals of the velocity fields. Then, the restriction of the harmonic maps and the extrema of the directional energy functionals is considered, Finally, we compute directional harmonic and biharmonic equations of the curvature vector fields to generalize total bending or energy of vector fields.

Keywords

• Directional energy functional
• directional energy minimizer
• harmonicity and biharmonicty

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