Jacobi vector fields and conjugate points on warped product manifolds

Dirmeier, Alexander; Scherfner, Mike; Shenawy, Sameh; Ünal, Bülent

doi:10.1016/s0034-4877(23)00043-5

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Warped Product Manifolds1

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2023

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“…Generalized Robertson-Walker space-time [22][23][24] I × f M 2 and standard static space-time [25][26][27] M 1 × f I are exceptional cases of Lorentzian warped product manifolds when a factor manifold is an open, connected interval of the real line. Warped product manifolds' scalar curvatures, Ricci curvatures, and Riemann curvatures can all be described in terms of the lift of the relevant curvature tensors from the factor manifolds to the product manifold [28][29][30].…”

Section: Warped Product Manifoldsmentioning

confidence: 99%

Projective Collineations in Warped Product Manifolds and (PRS)n Manifolds

Shenawy,

De,

Bin Turki

et al. 2023

Symmetry

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The current work first explores projective collineations on pseudo-Riemannian manifolds. Projective collineations, curvature collineations, and Ricci curvature collineations are examined in relation to one another. On warped product manifolds, the projective collineations of the form ζ=ζ1+ζ2 are investigated. We scrutinize various inheritance aspects in projective collineations from warped product manifolds to its factor manifolds. This provides, for example, a partially negative solution to Besse’s problem regarding the existence of Einstein warped product manifolds. Finally, Pseudo-Ricci symmetric space-times admitting projective collineations are investigated.

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