arXiv research

Characterizes biharmonic constant mean curvature surfaces in Killing submersions.

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 simply-connected Riemannian surfaces and give explicit models for many Killing submersion…

A Killing submersion is a Riemannian submersion from a 3-manifold to a surface, both connected and orientable, whose fibres are the integral curves of a Killing vector field, not necessarily unitary. The first part of this paper deals with the classification of all Killing submersions in terms of two geometric function…

Paper finds bounds for mean curvature in specific submersions.

New examples of solitons found using submersion techniques.

It is proved the existence and uniqueness of graphs with prescribed mean curvature in Riemannian submersions fibered by flow lines of a vertical Killing vector field.

Study of critical tori for mean curvature energies in Killing submersions.

Study local equivalence of Riemannian submersions using differential invariants.

We generalize Hadamard-Stoker-Currier Theorems for surfaces immersed in a Killing submersion over a strictly Hadamard surface whose fibers are the trajectories of a unit Killing field. We prove that every complete surface whose principal curvatures are greater than a certain function (depending on the ambient manifold)…

We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature orientable surfaces immersed in a Riemannian Killing submersion. As a consequence, the strong stability of such surfaces is studied. We also characterize constant mean curvature Hopf tori as the only ones att…

Study variations of metrics on Riemannian submersions to preserve fiber geometry.

Develops a duality for graphs in Riemannian and Lorentzian spaces with prescribed mean curvature.

The paper characterizes Clairaut conformal submersions on Ricci solitons.

We construct a twin correspondence between graphs with prescribed mean curvature in three-dimensional Riemannian Killing submersions and spacelike graphs with prescribed mean curvature in three-dimensional Lorentzian Killing submersions. Our duality extends the Calabi correspondence between minimal graphs in the Euclid…

We study focal points and Maslov index of a horizontal geodesic $γ:I\to M$ in the total space of a semi-Riemannian submersion $π:M\to B$ by determining an explicit relation with the corresponding objects along the projected geodesic $π\circγ:I\to B$ in the base space. We use this result to calculate the focal Maslov in…

We study constant mean curvature graphs in the Riemannian 3-dimensional Heisenberg spaces ${\cal H}={\cal H}(τ)$. Each such ${\cal H}$ is the total space of a Riemannian submersion onto the Euclidean plane $\mathbb{R}^2$ with geodesic fibers the orbits of a Killing field. We prove the existence and uniqueness of CMC gr…

A characterization of the Kerr-NUT-(A)de Sitter metric among four dimensional Λ-vacuum spacetimes admitting a Killing vector is obtained in terms of the proportionality of the self-dual Weyl tensor and a natural self-dual double two-form constructed from the Killing vector. This result recovers and extends a previous c…

Minimal graphs over non-compact domains in 3-manifolds solved with estimates and uniqueness results.

Local classification of 4D Ricci solitons with specific algebra properties.

The paper explores how non-Killing fields on internal spaces can produce massive gauge fields with chiral interactions.

Weyl's intrinsic volumes converge to the Euler characteristic of the base manifold under certain metrics.

The Lie group SO_0(n, 1) has the left-invariant metric coming from the Killing-Cartan form. The maximal compact subgroup SO(n) of the isometry group acts from the left. The geometry of the quotient space of the homogeneous submersion SO_0(n, 1) -> SO(n)\SO_0(n, 1) is investigated. The space is expressed as a warped pro…

We obtain an estimate for the norm of the second fundamental form of stable H-surfaces in Riemannian 3-manifolds with bounded sectional curvature. Our estimate depends on the distance to the boundary of the surface and on the bounds on the geometry of the ambient manifold but not on the manifold itself. We give some ap…

In this paper we will prove Hadamard-Stoker type theorems in the following ambient spaces: $\man ^n \times \r$, where $\man ^n $ is a $1/4-$pinched manifold, and certain Killing submersions, e.g., Berger spheres and Heisenberg spaces. That is, under the condition that the principal curvatures of an immersed hypersurfac…

Introduces singular Finsler foliations and their properties.

Solves Jenkins-Serrin problem in 3-manifolds with Killing vector fields.

Let $V^n$ be an open manifold of non-negative sectional curvature with a soul $Σ$ of co-dimension two. The universal cover $\tilde N$ of the unit normal bundle $N$ of the soul in such a manifold is isometric to the direct product $M^{n-2}\times R$. In the study of the metric structure of $V^n$ an important role plays t…

Sphere theorems extended to Riemannian foliations with new results on curvature and leaf spaces.

The paper classifies special surfaces in a 3D space.

Introduces new types of submersions from quaternionic Hermitian manifolds.

Study connects stationary spacetimes with pre-Randers metrics using Fermat's principle.

Study new submersion types on quaternionic manifolds.

The paper defines and explores Clairaut conformal submersions in Riemannian geometry.

Generalizes warped product submersion to conformal case.

Generalizes O'Neill's equations to pseudo-Finsler submersions.

The paper studies biharmonic submersions in Riemannian geometry.

The paper defines and studies conformal slant submersions in contact geometry.

We give a general Lie-theoretic construction for anti-invariant almost Hermitian Riemannian submersions, anti-invariant quaternion Riemannian submersions, anti-invariant para-Hermitian Riemannian submersions, anti-invariant para-quaternion Riemannian submersions, and anti-invariant octonian Riemannian submersions. This…

Bi-slant submersion generalizes slant and semi-slant submersion.

The paper studies conformal generic submersions from almost Hermitian manifolds.

The paper studies a new submersion type with specific conditions.

Study on Riemannian submersions from nearly Kaehler manifolds.

The paper characterizes submersions with Ricci soliton total manifolds and their properties.

Study anti-invariant submersions from holomorphic statistical manifolds.

Abstract: Characterizations for submersions to be harmonic or biharmonic shown; examples provided.

As a generalization of semi-invariant submersions, we introduce conformal semi-invariant submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a conformal submersion and show that there are certain product …

Study on geometric properties of h-conformal semi-invariant submersions.

Study of harmonic Riemannian submersions from 3D geometries.