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:

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

Tags

Tags

International impact, Reviewed
Změněno: 26/5/2023 12:01, Mgr. Marie Šípková, DiS.

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