Some results about concircular vector fields on Riemannian manifolds
Bang‐Yen Chen, Sharief Deshmukh
Abstract
In this article, we show that the presence of a concircular vector field on a Riemannian manifold can be used to obtain rigidity results for Riemannian and Kaehler manifolds. More precisely, we find new geometrical characterizations of spheres, Euclidean spaces as well as of complex Euclidean spaces using non-trivial concircular vector fields.
Topics & Concepts
MathematicsVector fieldPure mathematicsEuclidean geometryManifold (fluid mechanics)Rigidity (electromagnetism)Riemannian manifoldMathematical analysisGeometryStructural engineeringMechanical engineeringEngineeringAdvanced Differential Geometry ResearchGeometric Analysis and Curvature FlowsCosmology and Gravitation Theories