Projective curvature tensor on multiply warped product manifolds
QUAESTIONES MATHEMATICAE, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Publication Date: 2026
- Doi Number: 10.2989/16073606.2026.2733870
- Journal Name: QUAESTIONES MATHEMATICAE
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Istanbul University Affiliated: No
Abstract
We study the projective curvature tensor on multiply warped product manifolds. We investigate that the factor manifolds of a projectively flat multiply warped product manifold necessarily have constant sectional curvature. Moreover, we establish necessary and sufficient conditions under which such manifolds are projectively flat, symmetric, and admit a divergence-free curvature tensor. These results extend and generalize several earlier works in related geometric settings and highlight the deep interplay between curvature properties and the warping functions, which play a fundamental role in determining the geometric structure of the manifold.