Related papers: Tensor sphere bundle of Cheeger-Gromoll type

We obtain a class of locally symetric Kaehler Einstein structures on the nonzero cotangent bundle of a Riemannian manifold of positive constant sectional curvature. The obtained class of Kaehler Einstein structures depends on one essential…

We consider normal almost contact structures on a Riemannian manifold and, through their associated sections of an ad-hoc twistor bundle, study their harmonicity, as sections or as maps. We rewrite these harmonicity equations in terms of…

Is is known that the loop space associated to a Riemannian manifold admits a quasi-symplectic structure. This article shows that this structure is not likely to recover the underlying Riemannian metric by proving a result that is a strong…

Shape spaces are fundamental in a variety of applications including image registration, morphing, matching, interpolation, and shape optimization. In this work, we consider two-dimensional shapes represented by triangular meshes of a given…

We obtain a locally symmetric Kaehler Einstein structure on the cotangent bundle of a Riemannian manifold of negative constant sectional curvature. Similar results are obtained on a tube around zero section in the cotangent bundle, in the…

All invariant contact metric structures on tangent sphere bundles of each compact rank-one symmetric space are obtained explicitly, distinguishing for the orthogonal case those that are K-contact, Sasakian or 3-Sasakian. Only the tangent…

In the 3-dimensional Berwald-Moor space are bingles and tringles constructed, as additive characteristic objects associated to couples and triples of unit vectors - practically lengths and areas on the unit sphere. In analogy with the…

We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. We classify these structures by their intrinsic torsion and review the literature in terms of this scheme. Moreover, we determine necessary and…

The space of the structure (0,3)-tensors of the covariant derivatives of the structure endomorphism and the metric on almost contact B-metric manifolds is considered. A known decomposition of this space in orthogonal and invariant subspaces…

Among a family of 2-parameter left invariant metrics on Sp(2), we determine which have nonnegative sectional curvatures and which are Einstein. On the quotiente $\widetilde{N}^{11}=(Sp(2)\times S^4)/S^3$, we construct a homogeneous…

Natural metrics (Sasaki metric, Cheeger-Gromoll metric, Kaluza-Klein metrics etc.. ) on the tangent bundle of a Riemannian manifold is a central topic in Riemannian geometry. Generalized Cheeger-Gromoll metrics is a family of natural…

We prove that a compact contact threefold which is bimeromorphically equivalent to a Kaehler manifold and not rationally connected is the projectivised tangent bundle of a Kaehler surface.

We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit…

In this paper we consider a manifold $(M,\nabla )$ with a symmetric linear connection $\nabla $ which induces on the cotangent bundle $T^*M$ of $M$ a semi-Riemannian metric $\overline g$ with a neutral signature. The metric $\overline g$ is…

We undertake a systematic study of the infinitesimal geometry of the Thurston metric, showing that the topology, convex geometry and metric geometry of the tangent and cotangent spheres based at any marked hyperbolic surface representing a…

We consider a $3$-dimensional differentiable manifold with two circulant structures -- a Riemannian metric and an additional structure, whose third power is the identity. The structure is compatible with the metric such that an isometry is…

In this work we show that a Legendre transformation is nothing but a mere change of contact polarization from the point of view of contact geometry. Then, we construct a set of Riemannian and pseudo-Riemannian metrics on a contact manifold…

We show that Chern-Weil theory for tensor bundles over manifolds is a consequence of the existence of natural closed differential forms on total spaces of torsion free connections on frame bundles.

In this paper, we introduce a geometric structure called top, which is a trivialized bundle of plane pencils over a Riemannian 3-manifold, defined as the set of kernels of a circle of 1-forms (e.g. of contact and integrable forms) with…

We give a new proof that the completion of the Weil-Petersson metric on Teichm\"uller space is Gromov-hyperbolic if the surface is a five-times punctured sphere or a twice-punctured torus. Our methods make use of the synthetic geometry of…