arXiv subjects

Neiton Pereira da Silva

Publications and source records attributed to Neiton Pereira da Silva.

5 recordsLinked to original sources

arXiv2026

Equigeodesic vectors for homogeneous Riemannian submersions

We study $π$-equigeodesic vectors associated with homogeneous fibrations, namely vectors that are geodesic with respect to every homogeneous metric making the projection a Riemannian submersion. We obtain an algebraic criterion characterizing such vectors and apply it to classical flag manifolds and Ledger-Obata spaces. As a framework for this study, given Lie groups $K\subseteq H\subseteq G$ with $H$ and $K$ closed in $G$, and a fixed $G$-invariant metric $g_b$ on $G/H$, we describe the family of $G$-invariant metrics $g$ on $G/K$ for which the natural projection $π:(G/K,g)\to(G/H,g_b)$ is a Riemannian submersion. We also give a criterion for the fibers of $π$ to be totally geodesic.

math.DG↗

arXiv2024

Geometry of Invariant Almost Semi Kähler Submanifolds of Flag Manifolds

In this paper we discuss the geometry of homogeneous spaces witch are almost Hermitian submanifolds of flag manifolds. We prove that such spaces are necessarily minimal submanifolds and in the case where these submanifolds are also flag manifolds, they are totally geodesic.

math.DG↗

arXiv2019

G1 structures on flag manifolds

Let $U/K_Θ$ be a generalized flag manifold, where $K_Θ$ is the centralizer of a torus in $U$. We study $U$-invariant almost Hermitian structures on $U/K_Θ$. The classification of these structures are naturally related with the system $R_t$ of t-roots associated to $U/K_Θ$. We introduced the notion of connectedness by triples zero sum in a general set of linear functional and proved that t-roots are connected by triples zero sum. Using this property, the invariant G1 structures on $U/K_Θ$ are completely classified. We also study the Kähler form and classified the invariant quasi Kähler structures on $U/K_Θ$, in terms of t-roots.

math.DG↗

arXiv2016

Invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$

It is well known that the Einstein equation on a Riemannian flag manifold $(G/K,g)$ reduces to an algebraic system if $g$ is a $G$-invariant metric. In this paper we obtain explicitly new invariant Einstein metrics on generalized flag manifolds of $Sp(n)$ and $SO(2n)$; and we compute the Einstein system for generalized flag manifolds of type $Sp(n)$. We also consider the isometric problem for these Einstein metrics.

math.DG↗

arXiv2014

Isotropy summands and Einstein Equation of Invariant Metrics on Classical Flag Manifolds

It is well known that the Einstein equation on a Riemannian flag manifold $(G/K,g)$ reduces to a algebraic system, if $g$ is a $G$-invariant metric. In this paper we described this system for all flag manifolds of a classical Lie group. We also determined the number of isotropy summands for all of these spaces and proved certain properties of the set of t-roots for flag manifolds of type $B_n$, $C_n$ and $D_n$.

math.DG↗