We define a system of ODE that gives Einstein 4-dimensional metrics. We found new Ricci-flat incomplete metric of cohomogeneity 1 in explicit formulas and study its characteristics.
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8 results for “cohomogeneity-1”
Ricci flow converges to Taub-NUT metric under specific conditions.
problem Analyzing convergence of Ricci flow solutions to Taub-NUT metric.
method Study of Ricci flow starting from a specific metric on .
result Ricci flow converges to Taub-NUT metric in infinite time under certain conditions.
We survey the known existence and non-existence results for -instantons on non-compact cohomogeneity-1 -manifolds and their consequences, including an explicit example of a family of -instantons where bubbling, removable singularities and conservation of energy phenomena occur. We also describe several o…
Let G, a subset of O(4), act isometrically on the 3-sphere. In this article we calculate a lower bound for the diameter of the quotient spaces . We find it to be , which is exactly the value of the lower bound for diameters of the spherical space forms. In the p…
We study the Ricci flow on starting at an SU(2)-cohomogeneity 1 metric whose restriction to any hypersphere is a Berger metric. We prove that if has no necks and is bounded by a cylinder, then the solution develops a global Type-II singularity and converges to the Bryant soliton when su…
The study establishes a lower bound for vector field energy on spheres.
problem Finding a lower bound for the energy functional of vector fields on spheres.
method Analyzing the energy functional on compact Riemannian manifolds with specific geometric properties.
result The energy functional is bounded below by for -invariant vector fields on spheres with Ricci curvature lower bound .
Geodesics in symmetrized bidisc have intrinsic orthogonality and distinguished directions.
problem Understanding orthogonality and distinguished geodesics in the symmetrized bidisc under the Carathéodory metric.
method Analyzing the complex tangent bundle of the symmetrized bidisc, splitting it into sharp and flat bundles, and defining orthogonality and geodesics.
result Geodesics in the symmetrized bidisc are orthogonal to flat geodesics, and the space is foliated by geodesics orthogonal to a fixed flat geodesic.
Study on quaternionic Kähler manifolds and their integrable Hermitian structures.
problem Properties and integrability of quaternionic Kähler manifolds with Killing vector fields.
method Analysis of quaternionic Kähler manifolds with Killing vector fields, deriving conditions for integrability and conformal Kählerity.
result For a large class of quaternionic Kähler manifolds, the structure is integrable.