On a conformal $C$-Killing vector field in a compact Sasakian 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 =...

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...

Lightlike Submanifolds of a Para-Sasakian Manifold

In the present paper we study lightlike submanifolds of almost paracontact metric manifolds. We define invariant lightlike submanifolds. We study radical transversal lightlike submanifolds of para-Sasakian manifolds and investigate the geometry of distributions. Also we introduce a general notion of paracontact Cauchy-Riemann (CR) lightlike submanifolds and we derive some necessary and sufficie...