Holonomy algebras of pseudo-hyper-Kählerian manifolds of index 4

BEZVITNAYA, Natalia. Holonomy algebras of pseudo-hyper-Kählerian manifolds of index 4. Differential Geometry and its Applications. 2013, vol. 31, No 2, p. 284--299. ISSN 0926-2245. Available from: https://dx.doi.org/10.1016/j.difgeo.2012.11.001.

Basic information

• Original name: Holonomy algebras of pseudo-hyper-Kählerian manifolds of index 4
• Authors: BEZVITNAYA, Natalia (643 Russian Federation, guarantor, belonging to the institution).
• Edition: Differential Geometry and its Applications, 2013, 0926-2245.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Netherlands
• Confidentiality degree: is not subject to a state or trade secret
• Impact factor: Impact factor: 0.585
• RIV identification code: RIV/00216224:14310/13:00066089
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1016/j.difgeo.2012.11.001
• UT WoS: 000317448000010
• Keywords in English: Pseudo-hyper-Kählerian manifold; Holonomy algebra; Curvature tensor; Symmetric space
• Tags: AKR, rivok, ZR

Abstract

The holonomy algebra of a pseudo-hyper-Kählerian manifold of signature (4,4n+4) is a subalgebra of sp(1,n+1). Possible holonomy algebras of these manifolds are classified. Using this, a new proof of the classification of simply connected pseudo-hyper-Kählerian symmetric spaces of index 4 is obtained.

Links

• EE2.3.20.0003, research and development project: Name: Algebraické metody v geometrii s potenciálem k aplikacím
• GD201/09/H012, research and development project: Name: Algebraické a geometrické metody a struktury

Investor: Czech Science Foundation, Algebraic and geometric methods and structures