ON A CONFORMAL KILLING VECTOR FIELD IN A COMPACT ALMOST KAHLERIAN MANIFOLD

Completeness of Compact Lorentz Manifolds Admitting a Timelike Conformal Killing Vector Field

It is proved that every compact Lorentz manifold admitting a timelike conformai Killing vector field is geodesically complete. So, a recent result by Kamishima in J. Differential Geometry [37 (1993), 569-601] is widely extended. Recently, it has been proved in [2] that a compact Lorentz manifold of constant curvature admitting a timelike Killing vector field is (geodesically) complete. It is na...

Conformal vector fields and conformal transformations on a Riemannian manifold

In this paper first it is proved that if ξ is a nontrivial closed conformal vector field on an n-dimensional compact Riemannian manifold (M, g) with constant scalar curvature S satisfying S ≤ λ1(n − 1), λ1 being first nonzero eigenvalue of the Laplacian operator ∆ on M and Ricci curvature in direction of a certain vector field is non-negative, then M is isometric to the n-sphere S(c), where S =...

Conformal transformation in an almost Hermitian manifold

Abstract. In this paper, we have studied a conformal transformation between two almost Hermitian manifolds and shown that the associated Nijenhuis tensor is conformally invariant under this transformation. We have also discussed the properties of contravariant almost analytic vector field, covariant almost analytic vector field and some other properties in almost Hermitian manifold under this t...

The Conformal Transformation Group of a Compact Homogeneous Riemannian Manifold

Conformal Curvature Flows on Compact Manifold of Negative Yamabe Constant

Abstract. We study some conformal curvature flows related to prescribed curvature problems on a smooth compact Riemannian manifold (M, g0) with or without boundary, which is of negative (generalized) Yamabe constant, including scalar curvature flow and conformal mean curvature flow. Using such flows, we show that there exists a unique conformal metric of g0 such that its scalar curvature in the...