Earthline Journal of Mathematical Sciences

On Quasi-Generalized ϕ-recurrent Para-Kenmotsu Manifolds

N. Natesh, Vasanth Chavan, T. R. Shivamurthy, M. Nagaraja — Thu, 23 Jul 2026 00:00:00 +0000

The object of this paper is to study and reveal the various geometric properties of quasi-generalized $\phi-$recurrent (briefly, $\mathcal{QG}(\phi \mathcal{K}_{2n+1})$) para-Kenmotsu manifold. Among the results established here it is shown that a $\mathcal{QG}(\phi \mathcal{K}_{2n+1})$ para-Kenmotsu manifold is an Einstein manifold. Moreover, we prove that a Ricci soliton in a $\mathcal{QG}(\phi \mathcal{K}_{2n+1})$ para-Kenmotsu manifold is an expanding. Further, we study quasi-generalized $\mathcal{T}-\phi-$recurrent para-Kenmotsu manifold and obtain the results which reveal the nature of its associated 1-forms.

An Exponential-logarithmic Maximum Hardy-Hilbert-type Integral Inequality

Christophe Chesneau — Fri, 24 Jul 2026 02:28:40 +0000

This paper introduces a new variant of the Hardy-Hilbert integral inequality, referred to as an exponential-logarithmic maximum Hardy-Hilbert-type integral inequality. Using this result, we establish an additional related inequality. For completeness and accessibility, the paper is self-contained, and all proofs are provided in detail.

Geometric Quantization of Coadjoint Superorbits and Schrödinger-Fock Representations of the Heisenberg Supergroup

Aboubacar Nibirantiza — Fri, 24 Jul 2026 15:13:58 +0000

In the framework of Kirillov's orbit method for nilpotent supergroups, coadjoint superorbits of the Heisenberg supergroup naturally carry supersymplectic structures arising from the Kirillov-Kostant-Souriau form. Their geometric quantizationprovides a geometric realization of the irreducible unitary representations of the Heisenberg supergroup. In particular, after choosing an appropriate polarization, the resulting quantumstate space is identified with $L^2(\mathbb R^m)\otimes \Lambda^\bullet(\mathbb C^n),$ combining the bosonic Schrödinger representation with the fermionic Fock representation. Thus $\mathfrak h^{m|n}$ provides the simplest geometric model combining bosonic and fermionic quantization. The bosonic sector reproduces the canonical commutation relations, while the fermionic sector generates a Clifford algebra through anticommutation relations. This construction shows that Schrödinger-Fock representations arise naturally as the geometric quantization of coadjoint superorbits, thereby providing a deep connection between supergeometry, supersymplectic structures, and the representation theory of nilpotent supergroup. We begin by explicit calculations for the case $m=n=1$ and generalize to the arbitrary values of $m$ and $n$.

Some New Young-type Integral Inequalities

Christophe Chesneau — Mon, 27 Jul 2026 16:52:01 +0000

In this article, we present new forms of Young-type integral inequalities. Some of these extend the classical Young integral inequality by including a function and its inverse, while others introduce a function and its ratio transformation or derivative. The proofs of the main results are based on the standard Young product inequality and well-calibrated analytical tools, such as the Chasles integral formula and the Cauchy-Schwarz integral inequality, as well as changes of variables. Several inequalities also address the case where the main function is decreasing, thus expanding the traditional framework, which assumes an increasing function. In particular, the decreasing case leads to elegant formulations. Some theoretical aspects are illustrated with examples.