arXiv subjects

Özgür Kelekçi

Publications and source records attributed to Özgür Kelekçi.

7 recordsLinked to original sources

arXiv2026

Torsionful Killing-Yano Forms under T-Duality: Transformation Conditions and Emergent Isometries

We investigate the transformation of Killing-Yano (KY) $p$-forms under Abelian T-duality in the presence of a non-trivial three-form torsion. Using a torsionful, metric-compatible connection and the Buscher rules of T-duality, we derive compact, coordinate-free transformation laws applicable to KY forms of arbitrary degree under explicit matching assumptions. In particular, we show that a Killing 1-form is preserved by the direct duality map whenever its transverse components are independent of the isometry direction, with the dual circle component determined by a scalar correction equation. The framework is then applied to several examples, including the Hopf T-dual of $S^3$, Schwarzschild spacetime, and the Nappi-Witten plane wave with exact NS-NS torsion, where we analyze the transformed Killing-Yano forms explicitly. Finally, we give a generalized-geometric and double-field-theoretic interpretation of emergent Killing 1-forms in the T-dual geometry, showing how they arise from generalized Killing data in the original duality frame.

math-ph↗

arXiv2025

Spinor bilinears and Killing-Yano forms in generalized geometry

Spinor bilinears of generalized spinors and their properties are investigated. Generalized Killing and twistor spinor equations are considered and their relations to the equations satisfied by special types of differential forms are found. Killing equation in generalized geometry is written in terms of the generalized covariant derivative and Killing-Yano forms are described in the framework of generalized geometry. Construction of generalized Killing-Yano forms and generalized closed conformal Killing-Yano forms in terms of the spinor bilinears of generalized Killing spinors are determined.

hep-th↗

arXiv2025

Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion

We consider conformal Killing-Yano forms corresponding to the antisymmetric generalizations of conformal Killing vectors to higher degree forms in the presence of skew-symmetric torsion. Integrability conditions for torsionful conformal Killing-Yano forms are found and a graded Lie bracket for conformal Killing-Yano forms to constitute a graded Lie algebra structure is proposed. It is found that a graded Lie algebra structure for a special subset of torsionful conformal Killing-Yano forms can be constructed for a closed and parallel skew-symmetric torsion on constant curvature and Einstein manifolds. Similar structure for generalized hidden symmetries defined from generalized connection in generalized geometry is also constructed.

hep-th↗

arXiv2024

Minimal submanifolds and stability in Einstein manifolds

In this paper, we compute the index and nullity for minimal submanifolds of some complex Einstein spaces. We investigate the stability of these minimal submanifolds and suggest a criterion for instability for some cases. We also compute some higher eigenvalues for the Laplacian of the Berger spheres and provide with an algorithm.

math.DG↗

arXiv2023

Classification of Killing Magnetic Curves In H^3

In this paper, we study classification of magnetic curves corresponding to Killing vector fields of H^3 (hyperbolic 3-space). First, we solve the geodesic equation analytically. Then we calculate the trajectories generated by all the six Killing vector fields, which are considered as magnetic field vectors, by using perturbation method up to first order with respect to the strength of the magnetic field. We present a comparison of our solution with the numerical solution for one case. We also prove that 3-dimensional (α)-Kenmotsu manifolds cannot have any magnetic vector field in the direction of their Reeb vector fields.

math-ph↗

arXiv2022

On Kähler Structures of Taub-NUT and Kerr Spaces

In this paper, we study the Kählerian nature of Taub-NUT and Kerr spaces which are gravitational instanton and black hole solutions in general relativity. We show that Euclidean Taub-NUT metric is hyper-Kähler with respect to the usual almost complex structures by employing an alternative explicit coframe, and Euclidean Kerr metric is globally conformally Kähler. We also show that conformally scaled Euclidean Kerr space admits a Kähler structure by applying a conformal scaling factor stemming from the Lee-form of the original metric or alternatively a factor coming from self-dual part of the Weyl tensor $(W^+)$.

math.DG↗

arXiv2019

Locally conformally flat metrics on surfaces of general type

We prove a nonexistence theorem for product type manifolds. In particular we show that the 4-manifold $Σ_g\timesΣ_h$ does not admit any locally conformally flat metric arising from discrete and faithful representations for $g\geq 2$ and $h\geq 1$

math.DG↗