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Semi-symmetric four dimensional neutral Lie groups

Ali Haji-Badali, Amirhesam Zaeim (2020)

Czechoslovak Mathematical Journal

The present paper is concerned with obtaining a classification regarding to four-dimensional semi-symmetric neutral Lie groups. Moreover, we discuss some geometric properties of these spaces. We exhibit a rich class of non-Einstein Ricci soliton examples.

Singular BGG sequences for the even orthogonal case

Lukáš Krump, Vladimír Souček (2006)

Archivum Mathematicum

Locally exact complexes of invariant differential operators are constructed on the homogeneous model for a parabolic geometry for the even orthogonal group. The tool used for the construction is the Penrose transform developed by R. Baston and M. Eastwood. Complexes constructed here belong to the singular infinitesimal character.

Some properties of Carnot-Carathéodory balls in the Heisenberg group

Roberto Monti (2000)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Using the exact representation of Carnot-Carathéodory balls in the Heisenberg group, we prove that: 1. ∇ H n ⁡ d ⁢ z , t = 1 in the classical sense for all z , t ∈ H n with z ≠ 0 , where d is the distance from the origin; 2. Metric balls are not optimal isoperimetric sets in the Heisenberg group.

Spectral isolation of bi-invariant metrics on compact Lie groups

Carolyn S. Gordon, Dorothee Schueth, Craig J. Sutton (2010)

Annales de l’institut Fourier

We show that a bi-invariant metric on a compact connected Lie group G is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric g 0 on G there is a positive integer N such that, within a neighborhood of g 0 in the class of left-invariant metrics of at most the same volume, g 0 is uniquely determined by the first N distinct non-zero eigenvalues of its Laplacian (ignoring multiplicities). In the case where G is simple, N can be chosen to be two....

Split octonions and generic rank two distributions in dimension five

Katja Sagerschnig (2006)

Archivum Mathematicum

In his famous five variables paper Elie Cartan showed that one can canonically associate to a generic rank 2 distribution on a 5 dimensional manifold a Cartan geometry modeled on the homogeneous space G ˜ 2 / P , where P is one of the maximal parabolic subgroups of the exceptional Lie group G ˜ 2 . In this article, we use the algebra of split octonions to give an explicit global description of the distribution corresponding to the homogeneous model.

Stability of the geodesic flow for the energy

Eric Boeckx, José Carmelo González-Dávila, Lieven Vanhecke (2002)

Commentationes Mathematicae Universitatis Carolinae

We study the stability of the geodesic flow ξ as a critical point for the energy functional when the base space is a compact orientable quotient of a two-point homogeneous space.

Standard homogeneous Einstein manifolds and Diophantine equations

Yurii G. Nikonorov, Eugene D. Rodionov (1996)

Archivum Mathematicum

Some new examples of standard homogeneous Einstein manifolds with semisimple transitive groups of motions and semisimple isotropy subgroups are constructed. For the construction of these examples the solutions of some systems of Diophantine equations are used.

Structure of geodesics in weakly symmetric Finsler metrics on H-type groups

Zdeněk Dušek (2020)

Archivum Mathematicum

Structure of geodesic graphs in special families of invariant weakly symmetric Finsler metrics on modified H-type groups is investigated. Geodesic graphs on modified H-type groups with the center of dimension 1 or 2 are constructed. The new patterns of algebraic complexity of geodesic graphs are observed.

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