A note on Euclidean spheres.
Clifford hypersurfaces in a unit sphere.
Almost complex surfaces in the nearly Kähler .
Submanifolds of Euclidean space with parallel mean curvature vector.
Hopf hypersurfaces in nearly Kaehler 6-sphere.
Totally real surfaces in with parallel mean curvature vector.
Tangent bundle of the hypersurfaces in a Euclidean space.
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...
A note on conformal vector fields on a Riemannian manifold
We consider an n-dimensional compact Riemannian manifold (M,g) and show that the presence of a non-Killing conformal vector field ξ on M that is also an eigenvector of the Laplacian operator acting on smooth vector fields with eigenvalue λ > 0, together with an upper bound on the energy of the vector field ξ, implies that M is isometric to the n-sphere Sⁿ(λ). We also introduce the notion of φ-analytic conformal vector fields, study their properties, and obtain a characterization of n-spheres...
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