Invariant Connections with Skew-Torsion and Nabla-Einstein Manifolds

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.

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

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Germany
• Confidentiality degree: is not subject to a state or trade secret
• WWW: 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
• Tags: AKR, rivok
• Tags: International impact, Reviewed

Abstract

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