arXiv research

We propose a special deformation of the Sasaki metric on tangent and unit tangent bundle of a Hermitian locally symmetric manifold. Geodesics of this deformed metric have different projections on a base manifold for tangent or unit tangent bundle cases in contrast to usual Sasaki metric. Nevertheless, the projections o…

Geodesic flow mixing on convex projective manifolds proven.

Researchers found all invariant contact structures on tangent sphere bundles of compact symmetric spaces.

The study provides a lower bound for knot complement volumes related to geodesics.

The paper finds lower bounds for volumes of complex geometric structures.

Characterizes special curves on surface tangent bundles.

Study shows how certain foliations in unit tangent bundles behave.

Let $S^{n}$ be the $n$-sphere of constant positive curvature. For $n \geq 2$, we will show that a measure on the unit tangent bundle of $S^{2n}$, which is even and invariant under the geodesic flow, is not uniquely determined by its projection to $S^{2n}$.

Study on Ricci solitons on tangent and unit tangent bundles.

Unique entropy measure found for convex projective manifolds.

We show, using two different approaches, that there exists a family of Riemannian metrics on the tangent bundle of a two-sphere, which induces metrics of constant curvature on its unit tangent bundle. In other words, given such a metric on the tangent bundle of a two-sphere, the Hopf map is identified with a Riemannian…

We study the geometric properties of the base manifold for the unit tangent bundle satisfying the $η$-Einstein condition with the standard contact metric structure. One of the main theorems is that the unit tangent bundle of 4-dimensional Einstein manifold, equipped with the canonical contact metric structure, is $η$-E…

Study compact Kähler manifolds with pseudo-effective tangent bundles.

Knots in circle bundles are uniquely identified by their complements.

The paper classifies surfaces with pseudo-effective tangent bundles.

Projective manifolds with specific bundles are isomorphic to simpler spaces.

Researchers create metrics on hyperbolic space's tangent bundle.

The paper proves Morse estimates for translated points on unit tangent bundles.

Geodesics on modular surface yield arithmetic 3-manifolds.

In this paper we study a Riemanian metric on the tangent bundle $T(M)$ of a Riemannian manifold $M$ which generalizes Sasaki metric and Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to $T(M)$ a structure of locally conformal almost Kählerian manifold. This is th…

The paper studies smooth projective varieties with strictly nef tangent bundles and their properties.

Paper defines curvature equivalence for Legendre curves in a plane.

Study geodesics and F-geodesics on tangent bundles over para-Kähler-Norden manifolds.

Characterizes magnetic unit vector fields on Lie groups.

In this article we give a geometric interpretation of the Hitchin component for PSL(4,R) in the representation variety of a closed oriented surface of higher genus. We show that representations in the Hitchin component are precisely the holonomy representations of properly convex foliated projective structures on the u…

A contact metric manifold is said to be $H$-contact, if the characteristic vector field is harmonic. We prove that the unit tangent bundle of a Riemannian manifold $M$ equipped with the standard contact metric structure is $H$-contact if and only if $M$ is $2$-stein.

Geodesics of the same type on curved surfaces are randomly distributed.

Minimal vector fields on oscillator groups studied, with specific conditions for minimality.

Given a Hopf fibration of a round sphere by parallel great subspheres, we prove that the projection map to the base space is, up to isometries of domain and range, the unique Lipschitz constant minimizer in its homotopy class. Similarly, given a Hopf fibration of a round sphere by parallel great circles, we view a unit…

Establishes a correspondence between two mathematical identities.

The paper characterizes projective spaces and quadrics using strictly nef bundles.

Study harmonicity on tangent bundles with a specific metric.

Study on triviality of tangent and generalized tangent bundles of manifolds.

One says that a smooth manifold M is a pseudo-Riemannian manifold of signature (p,q) if the tangent bundle TM is equipped with a smooth non-degenerate symmetric inner product g of signature (p,q). Similarly one says that M is an affine manifold if TM is equipped with a torsion free connection. One says g is Osserman if…

New surfaces show horocyclic flow isn't always minimal.

Proves uniqueness of tangent cones for specific types of connections.

The study shows conditions for thermostats to have no conjugate points.

We prove that the geodesic flow on the unit tangent bundle to a hyperbolic 2-orbifold is left-handed if and only if the orbifold is a sphere with three conic points. As a consequence, on the unit tangent bundle to a 3-conic sphere, the lift of every finite collection of closed geodesics that is zero in integral homolog…

We consider the geodesic flow of reversible Finsler metrics on the 2-sphere and the 2-torus, whose geodesic flow has vanishing topological entropy. Following a construction of A. Katok, we discuss examples of Finsler metrics on both surfaces, which have large ergodic components for the geodesic flow in the unit tangent…

Unified study of surfaces using Clifford algebras.

Proves geodesic connections on 2-torus without invariant tori.

The paper proves structures for complex projective varieties with certain tangent bundle properties.

Study numerically flat foliations on Kähler manifolds, proving new splitting theorems.

Study on geodesics and dihedral groups in lattices.

Reconstructs tangent bundle of complex projective plane using tropical geometry.

The paper derives new Gauss-Bonnet formulas for frontal bundles over surfaces with boundary.

Study biharmonic vector fields and unit vector fields on Riemannian manifolds.

Study tangent cones of Hermitian-Yang-Mills connections and their relation to vector bundles.