CRITICAL POINTS AND WARPED PRODUCT METRICS

Warped product and quasi-Einstein metrics

Warped products provide a rich class of physically significant geometric objects. Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial quasi-Einstein warped product, and non compact complete base manifolds which do not admit any non-triv...

Warped Product Rigidity

In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. This warped product structure will be used to study warped product Einstein structures in [HPW3].

Warped Product Submanifolds of Riemannian Product Manifolds

and Applied Analysis 3 where TX and NX are the tangential and normal components of FX, respectively, and for V ∈ T⊥M,

Contact CR-Warped product submanifolds in Kenmotsu space forms

Abstract: In the present paper, we give a necessary and sufficient condition for contact CR-warped product to be contact CR-product in Kenmotsu space forms.

Small Points and Adelic Metrics