Related papers: Unit Killing Vector Fields on Nearly Kahler Manifo…

In this paper we have obtained evolution of some geometric quantities on a compact Riemannian manifold $M^n$ when the metric is a Yamabe soliton. Using these quantities we have obtained bound on the soliton constant. We have proved that the…

This paper is concerned with the existence of constant scalar curvature Kaehler metrics on blow ups at finitely many points of compact manifolds which already carry constant scalar curvature Kaehler metrics. We also consider the…

We consider a class of complete Kahler manifolds with a strictly pseudoconvex boundary at infinity. After studying its asymptotic geometry, we formulate a conjecture in the Kahler-Einstein case relating the bottom of spectrum to the CR…

In this paper, we investigate conformal Killing's vectors (CKVs) admitted by some plane symmetric spacetimes. Ten conformal Killing's equations and their general forms of CKVs are derived along with their conformal factor. The existence of…

We prove that any compact Cauchy horizon with constant non-zero surface gravity in a smooth vacuum spacetime is a smooth Killing horizon. The novelty here is that the Killing vector field is shown to exist on both sides of the horizon. This…

F-manifolds are complex manifolds with a multiplication with unit on the holomorphic tangent bundle with a certain integrability condition. Here the local classification of 3-dimensional F-manifolds with or without Euler fields is pursued.

Third rank Killing tensors in (1+1)-dimensional geometries are investigated and classified. It is found that a necessary and sufficient condition for such a geometry to admit a third rank Killing tensor can always be formulated as a…

A symmetric tensor field on a Riemannian manifold is called Killing field if the symmetric part of its covariant derivative is equal to zero. There is a one to one correspondence between Killing tensor fields and first integrals of the…

In this paper, we study the deformation limit of compact Kahler manifolds. We show that the limit to be a manifold in the Fujiki class C is equivalent to the finiteness of the upper volume. We also prove the Streets-Tian conjecture for a…

We study the structure of two-sided vector spaces over a perfect field $K$. In particular, we give a complete characterization of isomorphism classes of simple two-sided vector spaces which are left finite-dimensional. Using this…

In the extremal Kerr spacetime the horizon Killing vector field is null on a timelike hypersurface crossing the horizon at a fixed latitude, and spacelike on both sides of the horizon in the equatorial plane. We explain in some detail how…

Let $(M,J)$ be a $2n$-dimensional almost complex manifold and let $x\in M$. We define the notion of almost complex blow-up of $(M,J)$ at $x$. We prove the existence of almost complex blow-ups at $x$ under suitable assumptions on the almost…

The generalized Fierz identities are addressed in the K\"ahler-Atiyah bundle framework from the perspective of the equations governing constrained generalized Killing spinor fields. We explore the spin geometry in a Riemannian 8-manifold…

We consider 3- and 6-vector deformations of 11-dimensional supergravity backgrounds of the form $M_5\times M_6$ admitting at least 3 Killing vectors. Using flux formulation of the E${}_{6(6)}$ exceptional field theory we derive (sufficient)…

We study local automorphisms of holomorphic Cartan geometries. This leads to classification results for compact complex manifolds admitting Cartan geometries. We prove that a compact Calabi-Yau manifold bearing a holomorphic Cartan geometry…

We study some subsets of the Green-Lazarsfeld set $\Sigma^{1}(M)$ for a compact Kahler manifold $M$.

We couple n copies of N=(2,0) scalar multiplets to a gauged N=(2,0) supergravity in 2+1 dimensions which admits AdS_3 as a vacuum. The scalar fields are charged under the gauged R-symmetry group U(1) and parametrize certain Kahler manifolds…

This article studies germs of holomorphic vector fields at the origin of C3 that are tangent to holomorphic foliations of codimension one. Two situations are considered. First, we assume hypotheses on the reduction of singularities of the…

A rank $m$ symmetric tensor field on a Riemannian manifold is called a Killing field if the symmetric part of its covariant derivative is equal to zero. Such a field determines the first integral of the geodesic flow which is a degree $m$…

M-theory suggests the study of 11-dimensional space-times compactified on some 7-manifolds. From its intimate relation to superstrings, one possible class of such 7-manifolds are those that have Calabi-Yau threefolds as boundary. In this…