Contact metric manifolds with large automorphism group and (κ, µ)-spaces
Complex Manifolds, 2019 We discuss the classifiation of simply connected, complete (κ, µ)-spaces from the point of view of homogeneous spaces. In particular, we exhibit new models of (κ, µ)-spaces having Boeckx invariant -1.
Lotta Antonio
doaj +1 more source
Contact manifolds, Lagrangian Grassmannians and PDEs
Complex Manifolds, 2018 In this paper we review a geometric approach to PDEs. We mainly focus on scalar PDEs in n independent variables and one dependent variable of order one and two, by insisting on the underlying (2n + 1)-dimensional contact manifold and the so-called ...
Eshkobilov Olimjon +3 more
doaj +1 more source
A note on the uniqueness of the canonical connection of a naturally reductive space [PDF]
, 2012 We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere, a compact Lie
Olmos, Carlos, Reggiani, Silvio
core +3 more sources
On the Cartan Model of the Canonical Vector Bundles over Grassmannians
, 2006 We give a representation of canonical vector bundles over Grassmannian manifolds as non-compact affine symmetric spaces as well as their Cartan model in the group of the Euclidean motions.Comment: 6 ...
A. T. Fomenko +6 more
core +2 more sources
Corrigendum for "A geometric proof of the Karpelevich-Mostow theorem" [PDF]
, 2016 Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we give a counterexample and show how to avoid the use of this corollary to give a simpler proof of ...
Di Scala, Antonio J., Olmos, Carlos
core
Biharmonic and harmonic homomorphisms between Riemannian three dimensional unimodular Lie groups [PDF]
arXiv, 2020 We classify biharmonic and harmonic homomorphisms $f:(G,g_1)\rightarrow(G,g_2)$ where $G$ is a connected and simply connected three-dimensional unimodular Lie group and $g_1$ and $g_2$ are left invariant Riemannian metrics.
arxiv
Spherical Spectral Synthesis and Two-Radius Theorems on Damek-Ricci Spaces [PDF]
, 2008 We prove that spherical spectral analysis and synthesis hold in Damek-Ricci spaces and derive two-radius theorems.
arxiv +1 more source
Cohomogeneity One Three Dimensional Anti de Sitter Space, Proper and Nonproper Actions [PDF]
Differential Geom. Appl. 39 (2015), 93--112, 2014 In this paper we give a classification of closed and connected Lie groups, up to conjugacy in $Iso({\bf adS_3})$, acting by cohomogeneity one on the three dimensional anti de sitter space ${\bf adS_3}$. Then we determine causal characters of the orbits and the orbit spaces, up to homeomorphism, in both cases, proper and nonproper actions.
arxiv +1 more source
The existence of light-like homogeneous geodesics in homogeneous Lorentzian manifolds
, 2012 In previous papers, a fundamental affine method for studying homogeneous geodesics was developed. Using this method and elementary differential topology it was proved that any homogeneous affine manifold and in particular any homogeneous pseudo ...
Calvaruso +10 more
core +1 more source
Four-dimensional homogeneous critical metrics for quadratic curvature functionals [PDF]
arXiv, 2023 We determine all homogeneous metrics which are critical for some quadratic curvature functional in dimension four.
arxiv