Einstein Warped Products with Einstein Base and Fiber
M\'arcio Lemes de Sousa, Tib\'erio Bittencourt de Oliveira Martins, Carlos Rodrigues da Silva
TL;DR
This paper investigates Einstein warped product manifolds with Einstein base and fiber, deriving conditions for the entire manifold to be Einstein and explicitly solving for the warping function in hyperbolic space cases.
Contribution
It provides necessary and sufficient conditions for warped products with Einstein base and fiber to be Einstein, including explicit solutions for hyperbolic space bases.
Findings
Conditions for Einstein warped products with Einstein base and fiber
Explicit warping function for hyperbolic space base
Characterization of Einstein warped products
Abstract
We study Einstein riemannian manifolds endowed with a warped product structure. We focus on the case in which both the base and the fiber are Einstein manifolds and establish necessary and sufficient conditions for the warped product itself to be an Einstein manifold. Moreover, we explicitly determine the warping function when the base is the hyperbolic space.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Holomorphic and Operator Theory · Point processes and geometric inequalities