Related papers: Mixed Killing Vector Fields on the Cigar Ricci-Bou…
In a previous paper arXiv:0707.2775 [gr-qc] we showed that stationary asymptotically flat vacuum black hole solutions in 5 dimensions with two commuting axial Killing fields can be completely characterized by their mass, angular momentum, a…
The object of the present paper is to study some types of Ricci pseudosymmetric $(LCS)_n$-manifolds whose metric is Ricci soliton. We found the conditions when Ricci soliton on concircular Ricci pseudosymmetric, projective Ricci…
In this paper we study certain types of metrics such as Ricci soliton, $*$-conformal Ricci soliton in 3-dimensional trans-Sasakian manifold. First we have shown that a 3-dimensional trans-Sasakian manifold of type $(\alpha,\beta)$ admits a…
A gradient Ricci soliton is a triple $(M,g,f)$ satisfying $R_{ij}+\nabla_i\nabla_j f=\lambda g_{ij}$ for some real number $\lambda$. In this paper, we will show that the completeness of the metric $g$ implies that of the vector field…
In a paper (math.DG/0403528) we obtained explicit examples of Moishezon twistor spaces of some compact self-dual four-manifolds admitting a non-trivial Killing field, and also determined their moduli space. In this note we investigate…
We present a new approach to the study of vacuum spacetimes with a Killing symmetry. The central quantity in this approach is the exterior derivative of the Killing vector field, which is a test electromagnetic field. Considering the…
We consider geometric and supergravity Killing spinors and the spinor bilinears constructed out of them. The spinor bilinears of geometric Killing spinors correspond to the antisymmetric generalizations of Killing vector fields which are…
Killing horizons which can be such for two or more linearly independent Killing vectors are studied. We provide a rigorous definition and then show that the set of Killing vectors sharing a Killing horizon is a Lie algebra…
On a Hermitian manifold we construct a symmetric $(1,1)$- tensor $H$ using the torsion and the curvature of the Chern connection. On a compact balanced Hermitian manifold we find necessary and sufficient conditions in terms of the tensor…
The aim of this paper is characterize a class of contact metric manifolds admitting $\ast$-conformal Ricci soliton. It is shown that if a $(2n + 1)$-dimensional $N(k)$-contact metric manifold $M$ admits $\ast$-conformal Ricci soliton or…
In $N(k)$-contact metric manifolds and/or $(k,\mu)$-manifolds, gradient Ricci solitons, compact Ricci solitons and Ricci solitons with $V$ pointwise collinear with the structure vector field $\xi $ are studied.
We completely describe paracontact metric three-manifolds whose Reeb vector field satisfies the Ricci soliton equation. While contact Riemannian (or Lorentz\-ian) Ricci solitons are necessarily trivial, that is, $K$-contact and Einstein,…
We study the properties of Ricci curvature of ${\mathfrak{g}}$-manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between Ricci curvature of the manifold and the Ricci curvature of the…
We determine Killing vector fields on the $3$-dimensional space $\mathbb R^3$ endowed with a special diagonal metric.
In this paper we present some structural results on the Lie algebras of transitive isometry groups of a general compact homogenous Riemannian manifold with nontrivial Killing vector fields of constant length.
We study conformal Killing forms on compact 6-dimensional nearly K\"ahler manifolds. Our main result concerns forms of degree 3. Here we give a classification showing that all conformal Killing 3-forms are linear combinations of $d \omega$…
When spacetime torsion is present, geodesics and autoparallels generically do not coincide. In this work, the well-known method that uses Killing vectors to solve the geodesic equations is generalized for autoparallels. The main definition…
We mainly study 3-dimensional complete gradient Ricci solitons with positive sectional curvature, whose scalar curvature attains its maximum at some point. In section 2, we estimate the area growth of level sets and the volume growth of…
We study complete scalar-flat Kahler manifolds with a Killing field and a mild asymptotic condition. We show that topological and geometric rigidities exist that powerfully restrict the manifold's behavior at infinity. We create a rough…
We consider three-dimensional Lorentzian metrics that locally admit four independent Killing vectors. Their classification is summarized, and conditions for characterizing them are found. These consist of algebraic classification of the…