Pompeiu Sets in Compact Heisenberg Manifolds

Isometric actions of Heisenberg groups on compact Lorentz manifolds

We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions—those for which the dimension of the Heisenberg group is one less than the dimension of the manifold. The main result is a classification of codimension-one actions, under the assumption they are real-ana...

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...

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Nonexistence of Cusp Cross-section of One-cusped Complete Complex Hyperbolic Manifolds Ii

Long and Reid have shown that some compact flat 3-manifold cannot be diffeomorphic to a cusp cross-section of any complete finite volume 1-cusped hyperbolic 4-manifold. Similar to the flat case, we give a negative answer that there exists a 3-dimensional closed Heisenberg infranilmanifold whose diffeomorphism class cannot be arisen as a cusp cross-section of any complete finite volume 1-cusped ...

Completeness with Respect to the Probabilistic Pompeiu-hausdorff Metric

The aim of the present paper is to prove that the family of all closed nonempty subsets of a complete probabilistic metric space L is complete with respect to the probabilistic Pompeiu-Hausdorff metric H . The same is true for the families of all closed bounded, respectively compact, nonempty subsets of L. If L is a complete random normed space in the sense of Šerstnev, then the family of all n...