Liouville-type theorems for twisted and warped products manifolds
Sergey Stepanov
TL;DR
This paper establishes Liouville-type theorems that demonstrate the non-existence of certain complete twisted and warped product manifolds, extending previous results from compact cases to more general non-compact settings.
Contribution
It introduces new non-existence theorems for complete twisted and warped product manifolds, broadening the scope of Liouville-type results in differential geometry.
Findings
Proves non-existence of certain complete twisted product manifolds.
Extends Liouville-type theorems from compact to non-compact manifolds.
Provides conditions under which these manifolds cannot exist.
Abstract
In the present paper we prove Liouville-type theorems: non-existence theorems for complete twisted and warped products of Riemannian manifolds which generalize and complement similar results for compact manifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometry and complex manifolds