Characterizing Affine Vector Fields on Pseudo-Riemannian Manifolds

مقال فى مجلة

2024

We study the characteristics of affine vector fields on pseudo-Riemannian manifolds and provide tensorial formulas that characterize these vector fields. Using our approach, we present a straightforward proof that any affine vector field on a compact Riemannian manifold is a Killing vector field. Moreover, we establish several necessary and sufficient conditions for an affine vector field on a Riemannian manifold to be classified as a Killing or parallel vector field.

• نوع عمل المنشور: Article
• اسم الناشر: MDPIMDPI AG, Grosspeteranlage 5, CH-4052 BASEL, SWITZERLAND
• رقم المجلد: 13
• رقم الانشاء: 12