Related papers: Isometry groups of k-curvature homogeneous pseudo-…

For k at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). The curvature tensor of these manifolds is modeled on…

We construct a new family of curvature homogeneous pseudo-Riemannian manifolds modeled on $\mathbb{R}^{3k+2}$ for integers $k \geq 1$. In contrast to previously known examples, the signature may be chosen to be $(k+1+a, k+1+b)$ where $a,b…

For any k which is at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not k+1-affine curvature homogeneous, and hence not locally homogeneous. All the local scalar Weyl invariants…

The theory of harmonic vector fields on Riemannian manifolds is generalised to pseudo-Riemannian manifolds. Harmonic conformal gradient fields on pseudo-Euclidean hyperquadrics are classified up to congruence, as are harmonic Killing fields…

In this work we find the Killing vector fields of the riemannian submanifolds of the thermodynamic phase space of an ideal gas and show that the isometry group corresponding to them is homomorphic to the euclidean group $E(2)$. We also give…

We study all four-dimensional simply-connected indecomposable non-semisimple pseudo-Riemannian symmetric spaces whose metric has signature (2,2). We present models and compute their isometry groups. We solve the problem of the existence or…

Killing vector fields of constant length correspond to isometries of constant displacement. Those in turn have been used to study homogeneity of Riemannian and Finsler quotient manifolds. Almost all of that work has been done for group…

The study of symmetries in the realm of manifolds can be approached in two different ways. On one hand, Killing vector fields on a (pseudo-)Riemannian manifold correspond to the directions of local isometries within it. On the other hand,…

We study the relation between the existence of null conformal Killing vector fields and existence of compatible complex and para-hypercomplex structures on a pseudo-Riemannian manifold with metric of signature (2,2). We establish first the…

In this paper we develop new methods of study of generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres. We prove that for any…

The recently introduced Lipschitz-Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply…

We construct a family of balanced signature pseudo-Riemannian manifolds, which arise as hypersurfaces in flat space, that are curvature homogeneous, that are modeled on a symmetric space, and that are not locally homogeneous.

We show that the group of smooth isometries of a complemented sub-Riemannian manifold form a Lie group and establish dimension estimates based on the torsion of the canonical connection. We explore the interaction of curvature and the…

We prove the existence of compact pseudo-Riemannian manifolds with parallel Weyl tensor which are neither conformally flat nor locally symmetric, and represent all indefinite metric signatures in all dimensions $\,n\ge5$. Until now such…

We study the Lie algebra of infinitesimal isometries on compact Sasakian and K--contact manifolds. On a Sasakian manifold which is not a space form or 3--Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian…

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…

We investigate special Killing vector fields on 3-dimensional Riemannian manifolds of biwarped product-type. Starting from a diagonal metric on $\mathbb R^3$ determined by two nontrivial warping functions and a constant scaling factor, we…

A Killing submersion is a Riemannian submersion from an orientable 3-manifold to an orientable surface whose fibers are the integral curves of a unit Killing vector field in the 3-manifold. We classify all Killing submersions over…

In this paper, using connections between Clifford-Wolf isometries and Killing vector fields of constant length on a given Riemannian manifold, we classify simply connected Clifford-Wolf homogeneous Riemannian manifolds. We also get the…

It is known that a connected and simply-connected Lie group admits only one left-invariant Riemannian metric up to scaling and isometry if and only if it is isomorphic to the Euclidean space, the Lie group of the real hyperbolic space, or…