I. Chrysikos

activity

20092026

most citedInvariant Einstein metrics on flag manifolds with four isotropy summands

37 citations · 182 across the 24 of their papers we have counts for

collaborators

24 papers

math.DG2026

The canonical submersion of $S$ -manifolds and transverse Kähler-Einstein structures

Ioannis Chrysikos

This paper is devoted to the study of the holonomy properties of $(2 n + s)$ -dimensional $S$ -manifolds equipped with their characteristic connection. These structures genera…

math.DG2025

Adapted connections with skew-torsion on metric $f$ -manifolds

Aleksandra Borówka, Ioannis Chrysikos

We provide a natural higher-dimensional generalization of the adapted connections with skew-torsion on almost Hermitian and almost contact metric manifolds presented in \cite{FrIv}…

math.DG2022

Reductive homogeneous Lorentzian manifolds

Dmitri Alekseevsky, Ioannis Chrysikos, Anton Galaev

We study homogeneous Lorentzian manifolds $M = G / L$ of a connected reductive Lie group $G$ modulo a connected reductive subgroup $L$ , under the assumption that $M$ is (almost) $G$ -…

math.DG2021★ 2 cited

Differential geometry of $SO^{*} (2 n)$ -type structures -- Integrability

Ioannis Chrysikos, Jan Gregorovič, Henrik Winther

We study almost hypercomplex skew-Hermitian structures and almost quaternionic skew-Hermitian structures, as the geometric structures underlying $SO^{*} (2 n)$ - and $\maths…

math.DG2021

Decomposable $(5, 6)$ -solutions in eleven-dimensional supergravity

Hanci Chi, Ioannis Chrysikos, Eivind Schneider

We present decomposable (5,6)-solutions $M^{1, 4} \times M^{6}$ in eleven-dimensional supergravity by solving the bosonic supergravity equations for a variety of non-trivi…

math.DG2021★ 1 cited

Differential geometry of $SO^{*} (2 n)$ -type structures

Ioannis Chrysikos, Jan Gregorovič, Henrik Winther

We study $4 n$ -dimensional smooth manifolds admitting a $SO^{*} (2 n)$ - or a $SO^{*} (2 n) Sp (1)$ -structure, where $SO^{*} (2 n)$ is the quaternionic real for…

math.DG2020★ 5 cited

Ancient solutions of the homogeneous Ricci flow on flag manifolds

Stavros Anastassiou, Ioannis Chrysikos

For any flag manifold $M = G / K$ of a compact simple Lie group $G$ we describe non-collapsing ancient invariant solutions of the homogeneous unnormalized Ricci flow. Such solutions em…

math.DG2020

Homogeneous Einstein metrics on non-Kähler C-spaces

Ioannis Chrysikos, Yusuke Sakane

We study homogeneous Einstein metrics on indecomposable non-Kählerian C-spaces, i.e. even-dimensional torus bundles $M = G / H$ with $rank G > rank H$ over flag manifol…

math.DG2019

A note on the volume of $\nabla$ -Einstein manifolds with skew-torsion

Ioannis Chrysikos

We study the volume of compact Riemannian manifolds which are Einstein with respect to a metric connection with (parallel) skew-torsion. We provide a result for the sign of the fir…

math.DG2019★ 2 cited

Homogeneous 8-manifolds admitting invariant Spin(7)-structures

Dmitri Alekseevsky, Ioannis Chrysikos, Anna Fino +1

We study compact, simply connected, homogeneous 8-manifolds admitting invariant Spin(7)-structures, classifying all canonical presentations G/H of such spaces, with G simply connec…

math.DG2017★ 3 cited

A new $\frac{1}{2}$ -Ricci type formula on the spinor bundle and applications

Ioannis Chrysikos

Consider a Riemannian spin manifold $(M^{n}, g)$ $(n \geq 3)$ endowed with a non-trivial 3-form $T \in Λ^{3} T^{*} M$ , such that $\nabla^{c} T = 0$ , where $\nabla^{c}:=\nabla^{g}+\frac{1}{…

math.DG2016★ 6 cited

Invariant connections and $\nabla$ -Einstein structures on isotropy irreducible spaces

Ioannis Chrysikos, Christian O'Cadiz Gustad, Henrik Winther

This paper is devoted to a systematic study and classification of invariant affine or metric connections on certain classes of naturally reductive spaces. For any non-symmetric, ef…

math.DG2015★ 25 cited

Non-naturally reductive Einstein metrics on exceptional Lie groups

Ioannis Chrysikos, Yusuke Sakane

Given an exceptional compact simple Lie group $G$ we describe new left-invariant Einstein metrics which are not naturally reductive. In particular, we consider fibrations of $G$ ov…

math.DG2015★ 7 cited

Killing and twistor spinors with torsion

Ioannis Chrysikos

We study twistor spinors (with torsion) on Riemannian spin manifolds $(M^{n}, g, T)$ carrying metric connections with totally skew-symmetric torsion. We consider the characteristic…

math.DG2014★ 4 cited

Invariant connections with skew-torsion and $\nabla$ -Einstein manifolds

Ioannis Chrysikos

For a compact connected Lie group $G$ we study the class of bi-invariant affine connections whose geodesics through $e \in G$ are the 1-parameter subgroups. We show that the bi-inva…

math.DG2012★ 16 cited

Homogeneous Einstein metrics on generalized flag manifolds with five isotropy summands

Andreas Arvanitoyeorgos, Ioannis Chrysikos, Yusuke Sakane

We construct the homogeneous Einstein equation for generalized flag manifolds $G / K$ of a compact simple Lie group $G$ whose isotropy representation decomposes into five inequivalen…

math.DG2012★ 7 cited

The classification of homogeneous Einstein metrics on flag manifolds with $b_{2} (M) = 1$

Ioannis Chrysikos, Yusuke Sakane

Let $G$ be a simple compact connected Lie group. We study homogeneous Einstein metrics for a class of compact homogeneous spaces, namely generalized flag manifolds $G / H$ with secon…

math.DG2010

Homogeneous Einstein metrics on the generalized flag manifold Sp(n)/(U(p) x U(n-p))

Andreas Arvanitoyeorgos, Ioannis Chrysikos, Yusuke Sakane

We find the precise number of non-Kähler $S p (n)$ -invariant Einstein metrics on the generalized flag manifold $M = S p (n) / (U (p) \times U (n - p))$ with $n \geq 3$ and $1 \leq p \leq n - 1$ . We…

math.DG2010

Homogeneous Einstein metrics on G_2/T

Andreas Arvanitoyeorgos, Ioannis Chrysikos, Yusuke Sakane

We construct the Einstein equation for an invariant Riemannian metric on the exceptional full flag manifold $M = G_{2} / T$ . By computing a Gröbner basis for a system of polynomials of m…

math.DG2010★ 32 cited

The Ricci flow approach to homogeneous Einstein metrics on flag manifolds

Stavros Anastassiou, Ioannis Chrysikos

We give the global picture of the normalized Ricci flow on generalized flag manifolds with two or three isotropy summands. The normalized Ricci flow for these spaces descents to a…

math.DG2010★ 8 cited

Flag manifolds, symmetric $\fr{t}$-triples and Einstein metrics

Ioannis Chrysikos

Let $G$ be a compact connected simple Lie group and let $M=G^{\bb{C}}/P=G/K$ be a generalized flag manifold. In this article we focus on an important invariant of $G / K$ , the so cal…

math.DG2010★ 9 cited

Complete description of invariant Einstein metrics on the generalized flag manifold $S O (2 n) / U (p) \times U (n - p)$

Andreas Arvanitoyeorgos, Ioannis Chrysikos, Yusuke Sakane

We find the precise number of non-Kähler $S O (2 n)$ -invariant Einstein metrics on the generalized flag manifold $M = S O (2 n) / U (p) \times U (n - p)$ with $n \geq 4$ and $2 \leq p \leq n - 2$ . We…

math.DG2009★ 37 cited

Invariant Einstein metrics on flag manifolds with four isotropy summands

Andreas Arvanitoyeorgos, Ioannis Chrysikos

A generalized flag manifold is a homogeneous space of the form $G / K$ , where $K$ is the centralizer of a torus in a compact connected semisimple Lie group $G$ . We classify all flag…

math.DG2009★ 18 cited

Invariant Einstein metrics on generalized flag manifolds with two isotropy summands

Andreas Arvanitoyeorgos, Ioannis Chrysikos

Let $M = G / K$ be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group $G$ . We use the variational approach to find invariant Einstein metrics for…

The canonical submersion of S-manifolds and transverse Kähler-Einstein structures

Adapted connections with skew-torsion on metric f-manifolds

Reductive homogeneous Lorentzian manifolds

Differential geometry of SO∗(2n)-type structures -- Integrability

Decomposable (5,6)-solutions in eleven-dimensional supergravity

Differential geometry of SO∗(2n)-type structures

Ancient solutions of the homogeneous Ricci flow on flag manifolds

Homogeneous Einstein metrics on non-Kähler C-spaces

A note on the volume of ∇-Einstein manifolds with skew-torsion

Homogeneous 8-manifolds admitting invariant Spin(7)-structures

A new 21​-Ricci type formula on the spinor bundle and applications

Invariant connections and ∇-Einstein structures on isotropy irreducible spaces

Non-naturally reductive Einstein metrics on exceptional Lie groups

Killing and twistor spinors with torsion

Invariant connections with skew-torsion and ∇-Einstein manifolds

Homogeneous Einstein metrics on generalized flag manifolds with five isotropy summands

The classification of homogeneous Einstein metrics on flag manifolds with b2​(M)=1

Homogeneous Einstein metrics on the generalized flag manifold Sp(n)/(U(p) x U(n-p))

Homogeneous Einstein metrics on G_2/T

The Ricci flow approach to homogeneous Einstein metrics on flag manifolds

Flag manifolds, symmetric $\fr{t}$-triples and Einstein metrics

Complete description of invariant Einstein metrics on the generalized flag manifold SO(2n)/U(p)×U(n−p)

Invariant Einstein metrics on flag manifolds with four isotropy summands

Invariant Einstein metrics on generalized flag manifolds with two isotropy summands

The canonical submersion of $S$ -manifolds and transverse Kähler-Einstein structures

Adapted connections with skew-torsion on metric $f$ -manifolds

Differential geometry of $SO^{*} (2 n)$ -type structures -- Integrability

Decomposable $(5, 6)$ -solutions in eleven-dimensional supergravity

Differential geometry of $SO^{*} (2 n)$ -type structures

A note on the volume of $\nabla$ -Einstein manifolds with skew-torsion

A new $\frac{1}{2}$ -Ricci type formula on the spinor bundle and applications

Invariant connections and $\nabla$ -Einstein structures on isotropy irreducible spaces

Invariant connections with skew-torsion and $\nabla$ -Einstein manifolds

The classification of homogeneous Einstein metrics on flag manifolds with $b_{2} (M) = 1$

Complete description of invariant Einstein metrics on the generalized flag manifold $S O (2 n) / U (p) \times U (n - p)$