Related papers: Remarques sur les spineurs de Killing transversaux

We review properties of so-called special conformal Killing tensors on a Riemannian manifold $(Q,g)$ and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle $TQ$. We then address the question of generalizing this…

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time,…

In this note we give a criterion for the existence of a fractional-linear integral for a geodesic flow on a Riemannian surface and explain that modulo M\"obius transformations the moduli space of such local integrals (if nonempty) is either…

We study spin structures on Riemann and Klein surfaces in terms of divisors. In particular, we take a closer look at spin structures on hyperelliptic and $p$-gonal surfaces defined by divisors supported on their branch points. Moreover, we…

We construct Riemannian manifolds with completely integrable geodesic flows, in particular various nonhomogeneous examples. The methods employed are a modification of Thimm's method, Riemannian submersions and connected sums.

We prove long-time existence for mean curvature flow of a smooth $n$-dimensional spacelike submanifold of an $n+m$ dimensional manifold whose metric satisfies the timelike curvature condition.

We survey several problems concerning Riemannian manifolds with positive curvature of one form or another. We describe the PIC1 notion of positive curvature and argue that it is often the sharp notion of positive curvature to consider.…

We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.

In this paper the author determines necessary and sufficient conditions for existence of the Ehresmann connection on a manifold foliated by locally free action of the commutative Lie group. Also here we describe structure of $C_0(M)|_L$ for…

This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks,…

As a generalization of holomorphic submersions, anti-invariant submersions and slant submersions, we introduce slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give examples, obtain the existence conditions…

For supersymmetric spacetimes in eleven dimensions admitting a null Killing spinor, a set of explicit necessary and sufficient conditions for the existence of any number of arbitrary additional Killing spinors is derived. The necessary and…

Every Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fields (equivalently, every polynomial in the velocities…

We give a condition on the curvature tensors of Riemannian manifolds that admit Lipschitz approximation by polyhedral metrics with curvature bounded below or above. We show that this condition is also sufficient for the existence of local…

Semi-Riemannian manifolds that satisfy (homogeneous) linear differential conditions of arbitrary order on the curvature are analyzed. They include, in particular, the spaces with (higher-order) recurrent curvature, (higher-order) symmetric…

We develop a spinorial description of CR structures of arbitrary codimension. More precisely, we characterize almost CR structures of arbitrary codimension on (Riemannian) manifolds by the existence of a Spin$^{c, r}$ structure carrying a…

In this paper we determine conditions of existence of an induced Riemannian structure on the symplectic quotient of a symplectic and Riemannian manifold following the action of a Lie group acting upon it in a hamiltonian way with…

We study left-invariant symmetric Killing 2-tensors on 2-step nilpotent Lie groups endowed with a left-invariant Riemannian metric, and construct genuine examples, which are not linear combinations of parallel tensors and symmetric products…

Let M be a real Bott manifold with K\"{a}hler structure. Using Ishida characterization we give necessary and sufficient condition for the existence of the Spin-structure on M. In proof we use the technic developed in Popko, Szczepa\'{n}ski…

We establish necessary and sufficient conditions for existence of isometric immersions of a simply connected Riemannian manifold into a two-step nilpotent Lie group. This comprises the case of immersions into $H$-type groups.