Conformal geometry and spatially homogeneous cosmology
Conformal gradient vector fields on a compact Riemannian manifold
It is proved that if an n-dimensional compact connected Riemannian manifold (M,g) with Ricci curvature Ric satisfying 0 < Ric ≤ (n-1)(2-nc/λ₁)c for a constant c admits a nonzero conformal gradient vector field, then it is isometric to Sⁿ(c), where λ₁ is the first nonzero eigenvalue of the Laplacian operator on M. Also, it is observed that existence of a nonzero conformal gradient vector field on an n-dimensional compact connected Einstein manifold forces it to...
Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity
For odd-dimensional Poincaré–Einstein manifolds , we study the set of harmonic -forms (for ) which are (with ) on the conformal compactification of . This set is infinite-dimensional for small but it becomes finite-dimensional if is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology and the kernel of the Branson–Gover [3] differential operators on the conformal infinity . We also relate the set of forms in the kernel of to the conformal...
Conformal ℱ-harmonic maps for Finsler manifolds
By introducing the ℱ-stress energy tensor of maps from an n-dimensional Finsler manifold to a Finsler manifold and assuming that (n-2)ℱ(t)'- 2tℱ(t)'' ≠ 0 for any t ∈ [0,∞), we prove that any conformal strongly ℱ-harmonic map must be homothetic. This assertion generalizes the results by He and Shen for harmonics map and by Ara for the Riemannian case.
Conformal Imbeddings of the Complex Projective Plane and Self-Dual Connections.
Conformal indices of riemannian manifolds
Conformal Infinitesimal Transformations Of Almost Paracontact Metric Structures
Conformal invariant wave equations for spin zero and spin fields on de Sitter space
Conformal Jacobi operators of hypersurfaces in the de Sitter space.
Conformal Killing forms with normalisation condition
Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability
In this paper we investigate the geometry of conformal Killing graphs in a Riemannian manifold endowed with a weight function and having a closed conformal Killing vector field with conformal factor , that is, graphs constructed through the flow generated by and which are defined over an integral leaf of the foliation orthogonal to . For such graphs, we establish some rigidity results under appropriate constraints on the -mean curvature. Afterwards, we obtain some stability results...
Conformal Killing-Yano tensors on manifolds with mixed 3-structures.
Conformal mappings and the Plateau-Douglas problem in Riemannian manifolds.
Conformal metrics with constant -curvature.
Conformal metrics with prescribed scalar curvature.
Conformal nullity of isotropic submanifolds
We introduce and study submanifolds with extrinsic curvature and second fundamental form related by an inequality that holds for isotropic submanifolds and becomes equality for totally umbilical submanifolds. The dimension of umbilical subspaces and the index of conformal nullity of these submanifolds with low codimension are estimated from below. The corollaries are characterizations of extrinsic spheres in Riemannian spaces of positive curvature.
Conformal powers of the Laplacian via stereographic projection.
Conformal Ricci Soliton in Lorentzian -Sasakian Manifolds
In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian -Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian -Sasakian manifold admitting conformal Ricci soliton is -Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian -Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian -Sasakian...
Conformal scalar curvature on the hyperbolic space.
Conformal structures associated to generic rank 2 distributions on 5-manifolds -- characterization and Killing-field decomposition.