Search results for "Unit tangent bundle"

showing 2 items of 2 documents

On the volume of unit vector fields on spaces of constant sectional curvature

2004

A unit vector field X on a Riemannian manifold determines a submanifold in the unit tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. It is known that the parallel fields are the trivial minima.

Parallelizable manifoldGeneral MathematicsGEOMETRIA RIEMANNIANAMathematical analysisRiemannian manifoldSubmanifoldNormal bundleUnit tangent bundleMathematics::Differential GeometrySectional curvatureMathematics::Symplectic GeometryTangential and normal componentsTubular neighborhoodMathematics
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Actions de IR et courbure de ricci du Fibré unitaire tangent des surfaces

1986

Characterisation of 2-dimensional Riemannian manifolds (M, g) (in particular, of surfaces with constant gaussian curvatureK=1/c2, o,−1/c2, respectively) whose tangent circle bundle (TcM, gs) (gs=Sasaki metric) admit an «almost-regular» vector field belonging to an eigenspace of the Ricci operator.

Pure mathematicsGeneral MathematicsCircle bundleGaussianMathematical analysisTangentsymbols.namesakeUnit tangent bundlesymbolsVector fieldMathematics::Differential GeometryExponential map (Riemannian geometry)Ricci curvatureEigenvalues and eigenvectorsMathematicsRendiconti del Circolo Matematico di Palermo
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