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

We consider 6-dimensional strict nearly Kaehler manifolds acted on by a compact, cohomogeneity one automorphism group G. We classify the compact manifolds of this class up to G-diffeomorphisms. We also prove that the manifold has constant…

In this note we begin a systematic study of compact conformal manifolds of SCFTs in four dimensions (our notion of compactness is with respect to the topology induced by the Zamolodchikov metric). Supersymmetry guarantees that such…

We study Rarita-Schwinger fields on 6-dimensional compact strict nearly K\"{a}hler manifolds. In order to investigate them, we clarify the relationship between some differential operators for the Hermitian connection and the Levi-Civita…

In this article we study isometric immersions of nearly K\"ahler manifolds into a space form (specially Euclidean space) and show that every nearly K\"ahler submanifold of a space form has a totally umbilic foliation whose leafs are…

A three-dimensional Riemannian manifold has locally 6, 4, 3, 2, 1 or none independent Killing vectors. We present an explicit algorithm for computing dimension of the infinitesimal isometry algebra. It branches according to the values of…

We classify six-dimensional homogeneous nearly K\"{a}hler manifolds and give a positive answer to Gray and Wolf's conjecture: every homogeneous nearly K\"{a}hler manifold is a Riemannian 3-symmetric space equipped with its canonical almost…

Let $\mathbb{E}$ be a connected and orientable Riemannian 3-manifold with a non-singular Killing vector field whose associated one-parameter group of the isometries of $\mathbb{E}$ acts freely and properly on $\E$. Then, there exists a…

Let $D$ be a set of smooth vector fields on the smooth manifold $M$.It is known that orbits of $D$ are submanifolds of M. Partition $F$ of M into orbits of $D$ is a singular foliation. In this paper we are studying geometry of foliation…

We solve the Killing spinor equations of ${\cal N}=1$ supergravity, with four supercharges, coupled to any number of vector and scalar multiplets in all cases. We find that backgrounds with N=1 supersymmetry admit a null, integrable,…

Approximate Killing vector fields are expected to help define physically meaningful spins for non-symmetric black holes in general relativity. However, it is not obvious how such fields should be defined geometrically. This paper relates a…

We prove that any vector field on a three-dimensional compact manifold can be approximated in the C1-topology by one which is singular hyperbolic or by one which exhibits a homoclinic tangency associated to a regular hyperbolic periodic…

The existence of a nowhere zero real vector field implies a well-known restriction on a compact manifold. But all manifolds admit nowhere zero complex vector fields. The relation between these observations is clarified.

Euclidean special geometry has recently been investigated in the context of Euclidean supersymmetric theories with vector multiplets. In the rigid case, the scalar manifold is described by affine special para-Kahler geometry while the…

In this paper we introduce and study a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its various properties, prove the global existence of the solution of this…

In this paper we develop the basic tools for a classification of Killing vector fields of constant length on pseudo--riemannian homogeneous spaces. This extends a recent paper of M. Xu and J. A. Wolf, which classified the pairs $(M,\xi)$…

The existence of a vector field on a compact Kaehler manifold with nonempty zero locus and the properties of this zero locus strongly influence the geometry of the manifold. For example, J. Wahl proved that the existence of a vector field…

We provide conditions for a Riemannian manifold with a nontrivial closed affine conformal Killing vector field to be isometric to a Euclidean sphere or to the Euclidean space. Also, we formulate some triviality results for almost Ricci…

In this paper nontrivial Killing vector fields of constant length and corresponding flows on smooth complete Riemannian manifolds are investigated. It is proved that such a flow on symmetric space is free or induced by a free isometric…

A Theorem is proved which reduces the problem of completeness of orbits of Killing vector fields in maximal globally hyperbolic, say vacuum, space--times to some properties of the orbits near the Cauchy surface. In particular it is shown…

In this article, we show that a hypersurface of the nearly Kahler $CP^3$ or $F_{1,2}$ cannot have its shape operator and induced almost contact structure commute together. This settles the question for six-dimensional homogeneous nearly…