Geometry and complex manifolds

This paper addresses the spectral analysis of operators acting on reproducing kernel Hilbert spaces equipped with a semi-inner product induced by a positive operator $ \mathbb{A} $. A fundamental challenge in this setting is the geometric discrepancy between the normalized reproducing kernels and the unit $ \mathbb{A}…

• SELİM ÇETİN

The main topic of this paper is to characterize gradient $$\eta$$ -Ricci–Yamabe solitons on warped product manifolds. At first, we establish necessary and sufficient conditions under which a warped product manifold admits gradient $$\eta$$ -Ricci–Yamabe solitons. Next, we deduce the condition under which a warped prod…

To connect the biological activity of quantitative structure -activity (QSAR) and quantitative structure -property (QSPR) interactions, topological indices are employed in structural underpinnings with their physical attributes, such as strain energy, chromatic aberration, boiling point, melting point, stability, etc.…

We study random multivariate $P$-polynomials in $\mathbb{C}^d$ with monomial supports constrained to $nP\cap\mathbb{Z}_+^d$ for a convex body $P\subset\mathbb{R}_+^d$, and deterministic coefficients admitting a uniform exponential profile $f$ on $P$. Assuming the tail condition $\mathbb{P}(\log(1+|ξ_0|)>t)=o(t^{-d})$…

Abstract Let ( X , ω ) (X,\omega) be a compact Kähler manifold, ( L , h L ) (L,h^{L}) a positive line bundle, and ( E , h E ) (E,h^{E}) a Hermitian holomorphic vector bundle of rank 𝑟 on 𝑋. We prove that the pullback by the Kodaira embedding associated to L p ⊗ E L^{p}\otimes E of the 𝑘-th Chern form of the dual of th…

We initiate a systematic study of compactifications of type II string theory to two dimensions on Ricci-flat spaces with fluxes and sources. We derive universal constraints on such compactifications, and then develop type IIA compactifications on $\mathrm{Spin}(7)$-holonomy spaces with bulk fluxes whose tadpole is can…

We develop a variant of the barrier method in order to address questions about topology of Kostlan random real algebraic plane curves. In particular we prove that the expected number of connected components of the curve of length at least $\displaystyle{O\left(\sqrt{d^{-1}\log \log d}\right)}$ grows to infinity with $…

We develop a variant of the barrier method in order to address questions about topology of Kostlan random real algebraic plane curves. In particular we prove that the expected number of connected components of the curve of length at least $\displaystyle{O\left(\sqrt{d^{-1}\log \log d}\right)}$ grows to infinity with $…

The classical transversality lemma of contact geometry constructs a contact structure on a hypersurface transverse to a Liouville vector field using point-set topology and local flows. This paper translates the classical transversality lemma into the context of derived algebraic geometry and provides the derived Legen…

The classical transversality lemma of contact geometry constructs a contact structure on a hypersurface transverse to a Liouville vector field using point-set topology and local flows. This paper translates the classical transversality lemma into the context of derived algebraic geometry and provides the derived Legen…

Recently, the PTR-submanifold of an almost Hermitian manifold has been defined and studied as a large class including CR-submanifolds, hemi-slant submanifolds, and pointwise hemi-slant submanifolds, which are well-known in the literature. This novel category of submanifolds comprises two distributions, one of which is…

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