Compact gradient Einstein-type manifolds with boundary
Allan George de Carvalho Freitas, Jos\'e Nazareno Vieira Gomes
TL;DR
This paper investigates rigidity properties of compact gradient Einstein-type manifolds with boundary, leading to new characterizations of hemispheres, geodesic balls, and topological insights in specific dimensions.
Contribution
It provides novel rigidity results and characterizations for Einstein-type manifolds with boundary, especially in low dimensions, expanding understanding of their geometric and topological properties.
Findings
Characterization of hemispheres and geodesic balls in space forms
Topological characterizations of boundaries in dimensions three and five
Upper bounds for boundary area in specific dimensions
Abstract
We deal with rigidity results for compact gradient Einstein-type manifolds with nonempty boundaries. As a result, we obtain new characterizations for hemispheres and geodesic balls in simply connected space forms. In dimensions three and five, we obtain topological characterizations for the boundary and upper bounds for its area.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Point processes and geometric inequalities