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Gabriel-Eduard Vîlcu

Publications and source records attributed to Gabriel-Eduard Vîlcu.

6 recordsLinked to original sources
arXiv2026

A Rigidity Theorem for Flat Graph Hypersurfaces of Variable-Returns-to-Scale Cobb--Douglas Production Functions

We study graph hypersurfaces associated with higher-dimensional ($n>2$) Cobb--Douglas production functions with variable returns to scale. We prove a rigidity theorem showing that every flat model in this class is necessarily homogeneous. The proof relies on an affine dimension-reduction principle that transfers the higher-dimensional flatness condition to suitable two-dimensional restrictions. We then obtain a complete classification in the non-degree-one case: every such flat model is a power of a positive linear form. For degree one, we give a local structural description in terms of envelopes on the rank-one set, with linearity on open rank-zero regions. These results extend the two-input analysis recently developed in [8] to the higher-dimensional setting, where the degree-one case exhibits a genuinely different behavior.

math.DG↗
arXiv2022

Vaisman manifolds and transversally Kähler-Einstein metrics

We use the transverse Kähler-Ricci flow on the canonical foliation of a closed Vaisman manifold to deform the Vaisman metric into another Vaisman metric with a transverse Kähler-Einstein structure. We also study the main features of such a manifold. Among other results, using techniques from the theory of parabolic equations, we obtain a direct proof for the short time existence of the solution for transverse {\K}-Ricci flow on Vaisman manifolds, recovering in a particular setting a result of Bedulli, He and Vezzoni [J. Geom. Anal. 28, 697--725 (2018)], but without employing the Molino structure theorem. Moreover, we investigate Einstein-Weyl structures in the setting of Vaisman manifolds and find their relationship with quasi-Einstein metrics. Some examples are also provided to illustrate the main results.

math.DG↗
arXiv2019

Almost product structures on statistical manifolds and para-Kähler-like statistical submersions

The main purpose of the present work is to investigate statistical manifolds endowed with almost product structures. We prove that the statistical structure of a para-Kähler-like statistical manifold of constant curvature in the Kurose's sense is a Hessian structure. We also derive the main properties of statistical submersions which are compatible with almost product structures. The results are illustrated by several nontrivial examples.

math.DG↗
arXiv2019

Transverse Kähler-Ricci flow and deformations of the metric on the Sasaki space $T^{1,1}$

In this paper we investigate the possibility to obtain locally new Sasaki-Einstein metrics on the space $T^{1,1}$ considering a deformation of the standard metric tensor field. We show that from the geometric point of view this deformation leaves transverse and the leafwise metric intact, but changes the orthogonal complement of the Reeb vector field using a particular basic function. In particular, the family of metric obtained using this method can be regarded as solutions of the equation associated to the Sasaki-Ricci flow on the underlying manifold.

math-ph↗
arXiv2014

Inequalities for generalized normalized $δ$-Casorati curvatures of slant submanifolds in quaternionic space forms

In this paper we prove two sharp inequalities involving the normalized scalar curvature and the generalized normalized $δ$-Casorati curvatures for slant submanifolds in quaternionic space forms. We also characterize those submanifolds for which the equality cases hold. These results are a generalization of some recent results concerning the Casorati curvature for a slant submanifold in a quaternionic space form obtained by Slesar et al.: J. Inequal. Appl. 2014, 2014:123.

math.DG↗