Invariant Connections with Skew-Torsion and Nabla-Einstein
Manifolds

J 2016

Invariant Connections with Skew-Torsion and Nabla-Einstein Manifolds

CHRYSIKOS, Ioannis

Basic information

Original name

Invariant Connections with Skew-Torsion and Nabla-Einstein Manifolds

Authors

CHRYSIKOS, Ioannis (300 Greece, guarantor, belonging to the institution)

Edition

Journal of Lie Theory, Lemgo (Germany), Heldermann Verlag, 2016, 0949-5932

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.471

RIV identification code

RIV/00216224:14310/16:00094244

Organization unit

Faculty of Science

UT WoS

000377235700002

Keywords in English

Invariant connection with skew-symmetric torsion; naturally reductive space; Killing metric; del-Einstein structure

Abstract

V originále

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. We also provide examples of del(+/- 1)-Einstein structures for a class of compact homogeneous spaces M = G/K with two isotropy summands.

Links

GP14-24642P, research and development project

Name: Diracovy operátory s torzí a speciální geometrické struktury

Investor: Czech Science Foundation

Citovat

CHRYSIKOS, Ioannis. Invariant Connections with Skew-Torsion and Nabla-Einstein Manifolds. Journal of Lie Theory. Lemgo (Germany): Heldermann Verlag, 2016, vol. 26, No 1, p. 11-48. ISSN 0949-5932.

@article{1380306,
   author = {Chrysikos, Ioannis},
   article_location = {Lemgo (Germany)},
   article_number = {1},
   keywords = {Invariant connection with skew-symmetric torsion; naturally reductive space; Killing metric; del-Einstein structure},
   language = {eng},
   issn = {0949-5932},
   journal = {Journal of Lie Theory},
   title = {Invariant Connections with Skew-Torsion and Nabla-Einstein Manifolds},
   url = {https://www.heldermann.de/JLT/JLT26/JLT261/jlt26002.htm},
   volume = {26},
   year = {2016}
}

TY  - JOUR
ID  - 1380306
AU  - Chrysikos, Ioannis
PY  - 2016
TI  - Invariant Connections with Skew-Torsion and Nabla-Einstein Manifolds
JF  - Journal of Lie Theory
VL  - 26
IS  - 1
SP  - 11-48
EP  - 11-48
PB  - Heldermann Verlag
SN  - 09495932
KW  - Invariant connection with skew-symmetric torsion
KW  - naturally reductive space
KW  - Killing metric
KW  - del-Einstein structure
UR  - https://www.heldermann.de/JLT/JLT26/JLT261/jlt26002.htm
N2  - 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. We also provide examples of del(+/- 1)-Einstein structures for a class of compact homogeneous spaces M = G/K with two isotropy summands.
ER  -

CHRYSIKOS, Ioannis. Invariant Connections with Skew-Torsion and Nabla-Einstein Manifolds. \textit{Journal of Lie Theory}. Lemgo (Germany): Heldermann Verlag, 2016, vol.~26, No~1, p.~11-48. ISSN~0949-5932.

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