Invariant Connections with Skew-Torsion and del-Einstein Manifolds
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F16%3A00094244" target="_blank" >RIV/00216224:14310/16:00094244 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—
Alternative languages
Result language
angličtina
Original language name
Invariant Connections with Skew-Torsion and del-Einstein Manifolds
Original language description
For a compact connected Lie group G we study the class of bi-invariant affine connections whose geodesics through e is an element of G are the 1-parameter subgroups. We show that the bi-invariant affine connections which induce derivations on the corresponding Lie algebra g coincide with the bi-invariant metric connections. Next we describe the geometry of a naturally reductive space (M = G/K, g) endowed with a family of G-invariant connections del(alpha) whose torsion is a multiple of the torsion of the canonical connection del(c). For the spheres S-6 and S-7 we prove that the space of G(2) (respectively, Spin(7))-invariant affine or metric connections consists of the family del(alpha). Then we examine the "constancy" of the induced Ricci tensor Ric(alpha) and prove that any compact isotropy irreducible standard homogeneous Riemannian manifold, which is not a symmetric space of Type I, is a del(alpha)-Einstein manifold for any alpha is an element of R.
Czech name
—
Czech description
—
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—
Result continuities
Project
<a href="/en/project/GP14-24642P" target="_blank" >GP14-24642P: Dirac operators with torsion and special geometric structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Lie Theory
ISSN
0949-5932
e-ISSN
—
Volume of the periodical
26
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
38
Pages from-to
11-48
UT code for WoS article
000377235700002
EID of the result in the Scopus database
—