arXiv research

Classifies conformal Killing 3-forms on nearly Kähler manifolds.

Study classifies manifolds with nonpositive curvature and finds conformal Killing forms.

Study finds only complex 2-step nilpotent Lie groups have Killing-Yano forms.

The paper describes 4D Riemannian manifolds with non-parallel Killing 2-forms.

Study Minkowski formula for conformal Killing-Yano 2-forms in constant curvature spacetimes.

A 2-form on a quaternionic-Kahler manifold (M, g) is called compatible (with the quaternionic structure) if it is a section of the direct sum bundle S^2(H) \oplus S^2(E). We construct a connection D on S^2(H) \oplus S^2(E)\oplus TM, which is a prolongation of the conformal-Killing operator acting on compatible 2-forms.…

Study of conformal Killing 2-forms on 4D Lie groups.

Researchers solve conformal Killing forms on Kaehler manifolds.

Study invariant CKY 2-forms on 5D Lie groups, classifying and determining their properties.

We prove that a compact quaternionic-Kähler manifold of dimension $4n\geq 8$ admitting a conformal-Killing 2-form which is not Killing, is isomorphic to the quaternionic projective space, with its standard quaternionic-Kähler structure.

Motivated by the possible characterization of Sasakian manifolds in terms of twistor forms, we give the complete classification of compact Riemannian manifolds carrying a Killing vector field whose covariant derivative (viewed as a 2-form) is a twistor form.

Classifies all toric Kahler surfaces with twistor 2-forms.

On a closed, connected Riemannian manifold with a Kähler foliation of codimension $q=2m$, any transverse Killing $r\ (\geq 2)$-form is parallel (S. D. Jung and M. J. Jung [\ref{JJ2}], Bull. Korean Math. Soc. 49 (2012)). In this paper, we study transverse conformal Killing forms on Kähler foliations and prove that if th…

Classifies ambitoric 4-orbifolds with completeness assumptions.

Study Killing forms on 2-step nilpotent Lie groups, finding their structure and dimensions.

Estimates quasi-local mass using Minkowski formula and conformal Killing-Yano forms.

Given a maximally non-integrable 2-distribution ${\mathcal D}$ on a 5-manifold $M$, it was discovered by P. Nurowski that one can naturally associate a conformal structure $[g]_{\mathcal D}$ of signature (2,3) on $M$. We show that those conformal structures $[g]_{\mathcal D}$ which come about by this construction are c…

Charge measurements for instantons and gravitational perturbations.

Geometric correspondence between quadrics and their twistor spaces for null foliations.

Study compares two pseudo-Kähler structures on a specific mathematical component.

In some other context, the question was raised how many nearly Kähler structures exist on the sphere $§^6$ equipped with the standard Riemannian metric. In this short note, we prove that, up to isometry, there exists only one. This is a consequence of the description of the eigenspace to the eigenvalue $λ= 12$ of the L…

Study local equivalence of Riemannian submersions using differential invariants.

Solves equivalence problem for 2-forms in 4 variables.

We study the relationship between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, which leads to a new approach to the infinitesimal description of multiplicative 2-forms and to the integration of twisted Dirac manifolds.

We extend the Mason-Newman Lax pair for the elliptic complex Monge-Ampère equation so that this equation itself emerges as an algebraic consequence. We regard the function in the extended Lax equations as a complex potential. We identify the real and imaginary parts of the potential, which we call partner symmetries, w…

Proves magnetic geodesic flow on sphere is integrable with constant 2-form.

Study magnetic fields on special Lie groups, proving non-existence of certain types.

The paper constructs non-convergent solutions to Vafa-Witten equations with specific harmonic 2-form limits.

Establishes a connection between Kähler metrics and vector bundle sections.

Study on harmonic forms on K3 surfaces converging to a flat 4D orbifold.

The paper classifies topological properties of specific geometric forms on manifolds.

We will prove a Moser-type theorem for self-dual harmonic 2-forms on closed 4-manifolds, and use it to classify local forms on neighborhoods of singular circles on which the 2-form vanishes. Removing neighborhoods of the circles, we obtain a symplectic manifold with contact boundary - we show that the contact form on e…

This paper explains a 2-form on moduli spaces using quasi-Hamiltonian and Dirac geometry.

The paper studies symplectic structures on character varieties of Sasakian threefolds.

Deforms Poisson quasi-Nijenhuis manifolds using closed 2-forms.

Sharp curl-Sobolev inequality solved on S^n and R^n.

The paper extends the classification of bi-invariant 2-forms to infinite-dimensional Lie groups.

We study the construction and classification of weakly Bochner-flat (WBF) metrics (i.e., Kahler metrics with coclosed Bochner tensor) on compact complex manifolds. A Kahler metric is WBF if and only if its `normalized' Ricci form is a hamiltonian 2-form: such 2-forms were introduced and studied in previous papers in th…

Killing-Yano and conformal Killing-Yano superalgebras are rigid in constant curvature manifolds.

Generalizes Lie algebra of conformal Killing vector fields to conformal Killing-Yano forms.

New method finds global Lagrangians for variational systems.

Killing tensors on complex projective space are identified and generated by Killing fields.

Researchers found indecomposable Killing tensor fields on quaternionic projective spaces.

Characterizes conformal Killing tensors and their Killing scales.

This paper is concerned with symmetries of closed multiplicative 2-forms on Lie groupoids and their infinitesimal counterparts. We use them to study Lie group actions on Dirac manifolds by Dirac diffeomorphisms and their lifts to presymplectic groupoids, building on recent work of Fernandes-Ortega-Ratiu \cite{FOR} on P…

The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is…

We introduce the notion of a hamiltonian 2-form on a Kaehler manifold and obtain a complete local classification. This notion appears to play a pivotal role in several aspects of Kaehler geometry. In particular, on any Kaehler manifold with co-closed Bochner tensor, the (suitably normalized) Ricci form is hamiltonian, …

Given an d-dimensional manifold with two commuting Killing vectors, together with an d - 1 dimensional submanifold in which one of the Killing vectors lies, then the lapse and shift of the second Killing vector, relative to this slice, remain constant along the orbits of the `surface' Killing vector. Alternatively, the…